ECE 216 LabManual Sept 2021
pdf
keyboard_arrow_up
School
University of Victoria *
*We aren’t endorsed by this school
Course
216
Subject
Electrical Engineering
Date
Apr 3, 2024
Type
Pages
58
Uploaded by btacc
L
ABORATORY M
ANUAL
ECE
216
E
LECTRICITY AND M
AGNETISM
September 2021
Course Instructor: Levi Smith
Department of Electrical and Computer Engineering
University of Victoria
Copyright © 2021, Department ECE, University of Victoria, BC, Canada.
i
Table of Contents Table of Contents
.....................................................................................................................
I
Laboratory and Manual Information
.....................................................................................
III
Laboratory Report Cover Sheet
....................................................................................
IV
Acknowledgement
.........................................................................................................
V
Preparation
....................................................................................................................
VI
Experiment 1 — Electrostatics
...............................................................................................
1
Experiment 1.1 −
Electrostatic Charges
.........................................................................
1
Equipment
...............................................................................................................
1
Introduction
.............................................................................................................
1
A – Conservation of Charge
....................................................................................
1
B – Distribution of Charge
......................................................................................
8
Experiment 1.2 −
Capacitance
......................................................................................
17
Equipment
.............................................................................................................
17
Introduction
...........................................................................................................
17
Theory
...................................................................................................................
17
Setup
.....................................................................................................................
18
Procedure A: The Effect of the Plate Separation
..................................................
20
Analysis A
.............................................................................................................
20
Procedure B: The Effect of a Dielectric Between the Plates
................................
21
Conclusions
...........................................................................................................
22
Experiment 2 — Magnetic Fields of Coils
...........................................................................
24
Equipment
.............................................................................................................
24
ii
Introduction
...........................................................................................................
24
Theory
...................................................................................................................
24
Setup
.....................................................................................................................
26
Single Coil Procedure
...........................................................................................
28
Analysis 1: Single Coil
.........................................................................................
29
Helmholtz Coil Setup
............................................................................................
29
Helmholtz Coil Procedure
.....................................................................................
31
Solenoid Procedure
...............................................................................................
31
Solenoid Field
.......................................................................................................
32
Magnetic Field across a Single Coil
.....................................................................
33
Experiment 3 — Faraday’s Law of Induction
.......................................................................
34
Equipment
.............................................................................................................
34
Introduction
...........................................................................................................
34
A – Faraday's Law
.................................................................................................
35
B – Lens’ Law Analysis
........................................................................................
39
C – Conservation of Energy
..................................................................................
42
Experiment 4 — Ampere’s Law
............................................................................................
47
Equipment
.............................................................................................................
47
Introduction
...........................................................................................................
47
Theory
...................................................................................................................
48
Setup
.....................................................................................................................
48
Procedure A: Path Encloses Current
.....................................................................
50
Procedure B: Path Does Not Enclose Current
......................................................
50
Analysis
.................................................................................................................
51
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
iii
L
ABORATORY AND M
ANUAL I
NFORMATION
The laboratory experiments are intended as a practical demonstration of various concepts introduced during regular classes. Due to the rigid timetable of the laboratory periods, it may happen on occasion that an experiment precedes the class material. This manual is intended as self-
contained study material, which will allow students to be prepared in advance for a laboratory experiment irrespective of material covered in class. All calculations and designs not requiring experimental results should be done prior to the laboratory period. To assess the degree of understanding of theory and procedures, a short oral or written test may be conducted by the instructor and used as a grading component.
Equipment pertaining to each lab setup will be described at the beginning of experiments sections. Students should familiarize themselves with the theory and operation of the laboratory equipment.
A laboratory report is required from each group for each experiment performed and shall be submitted within one week after the experiment. The front page of the report is shown in Fig. 0-1 and should be reproduced for each laboratory report.
The report should be divided into the following parts: objective, introduction, result, discussion and conclusion. The following are some points you should consider while preparing your lab report:
1.
Appearance
-
Does the report look professional?
2.
Presentation
-
Is your write-up easy to follow, logical and complete?
-
Did you make an effort to write your report in precise and concise style? Get other members of your group to read the manuscript before submission.
-
Did you make efficient use of relevant figures and tables?
-
Are the tables used clearly described?
-
Are graphs properly labelled (titles, units, etc.)?
-
Are proper headings used?
3.
Technical Contents
-
Are all required points covered?
-
Did you attempt to make some nontrivial observations and measurements on your own?
-
How well did you justify your conclusions and results?
-
Did you use consistently proper units?
4.
Punctuality
-
Do you adhere to the schedule for labs and submission of lab reports?
5.
Remember
-
A report represents written communication. Keep in mind the reader's perspective when writing your report.
iv
Department of Electrical and Computer Engineering University of Victoria
ECE 216 – Electricity and Magnetism
L
ABORATORY R
EPORT C
OVER S
HEET
Experiment No.:
____________________________________________________________ Title:
____________________________________________________________ Date of Experiment:
____________________________________________________________ (should be as scheduled)
Report Submitted on:
____________________________________________________________ (should be within one week from the time of experiment)
To:
____________________________________________________________ Laboratory Group #:
____________________________________________________________ Names: (please print)
____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ Fig. 0-1: The front page of a lab report.
v
Acknowledgement
This introduction on Laboratory and Manual Information is an abbreviated version of the respective section in the ECE 300 Lab Manual, originally written by the late Dr. A. Zielinski.
The original version of this manual (May 2021) was compiled by: Deisy Formiga Mamedes, Dr. P. So, and Dr. J. Bornemann.
All following sections describing four experiments have been copied/modified from suggested notes on pre-packaged experiments by PASCO:
https://www.pasco.com/subjects/college-physics/c/50.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
vi
Preparation Pasco Capstone is a software for data collection and analysis, and it will be used for all experiments. You will use it to collect the data from the sensors. The sensors are connected to Capstone through Bluetooth, the computer must have a Bluetooth connection. You will be able to insert the data in graph, table and digits display.
Capstone is available for Mac and Windows users and you can download it in: https://www.pasco.com/products/software/capstone#downloads-panel
The software manual is available in: https://www.pasco.com/help/capstone/index.html It is important to get familiar with the software interface before the experiment starts.
1
E
XPERIMENT 1
—
E
LECTROSTATICS
Experiment 1.1 −
Electrostatic Charges
Equipment
1
Basic Electrometer
ES-9078 1
Charge Producers and Proof Plane
ES-9057C 1
Faraday Ice Pail and Shield
ES-9042A 1
Conductive Spheres, 13 cm
ES-9059C
1
Conductive Shapes
ES-9061 1
Electrostatics Voltage Source
ES-9077 Introduction
The purpose of part A of this experiment is to compare and contrast the results of three different methods of charging: (1) rubbing two objects together; (2) touching a charged object to a neutral one (charging by contact); and (3) grounding a neutral object while it is polarized (charging by induction).
Part A will also demonstrate the law of conservation of charge.
The purpose of part B of this experiment is to investigate how charge distributes on the outer surfaces of a spherical conductor and on the outer surface of a non-spherical conductor. The charge distribution inside the spherical conductor will also be examined.
A – Conservation of Charge
Theory A
Electric Charges
Electric charge is a fundamental property of nature. It comes in two types, called positive and negative. Positive charge is the type of charge carried by protons. Negative charge is the type of charge carried by electrons. As nearly as can be measured (better than 1 part in 10
30
), the magnitude of the charge on an electron is the same as the magnitude of the charge on a proton. Atoms normally have the same number of protons and electrons and this balance of charges makes them electrically neutral. Most objects are found in this neutral state. For an object to be positively charged, it has to have more protons than electrons. For an object to be negatively charged, it has to have more electrons than protons, disturbing the neutral charge balance.
Forces between Charges
Opposite charges always attract. Like charges tend to repel. At an elemental level, like charges always repel (electrons repel electrons, protons repel protons), but for macroscopic objects, non-
symmetric charge distribution can result in an overall attraction between two objects that carry the
2
same type of overall charge (positive or negative). Non-symmetrical charge distribution always results in an attraction between a charged object and an electrically neutral (overall) object.
Charging: all charging processes involve the transfer of electrons from one object to another. In order for an object to become positively charged, it must lose some of its electrons. In order for an object to become negatively charged, it must acquire more electrons. 1.
Charging by rubbing
: When two initially neutral non-conducting objects are rubbed together, one of them will generally bind electrons more strongly than the other and take electrons from the other. The law of conservation of charge requires that the total amount of electrons be conserved. That is, electrons only move from one object to another, but no new electrons are created, nor do they disappear. Overall, the two objects when considered together still have zero net charge.
2.
Charging by contact
: When a charged object is touched to a neutral (or less charged) object, repulsive forces between the like charges result in some of the charge transferring to the less charged object so the like charges will be further apart. This effect is much larger for conducting objects.
3.
Charging by induction
: The protons and electrons inside any object respond to electric forces of attraction or repulsion. When an object is placed near a charged object, the charged object will exert opposite forces on the protons and the electrons inside the other object, forcing them to move apart from each other. One side of the object will become more positive than it was initially. The other side will become more negative, as electrons migrate internally. This condition is called polarization
, a word that refers to the object having “poles,” or opposite sides with different electrical states, even though the object as a whole may still be neutral. If a conductor is touched to the polarized object, some of the charge will transfer to the conductor. If the conductor is then removed, the object now carries a net charge different from its initial charge. For example, consider the sequence in Fig. 1-1. Fig. 1-1a shows an isolated neutral conductor. In Fig. 1-1b, a negatively charged object has been placed near the neutral conductor, which is now polarized. Another conductor (elliptical) is shown but is not yet involved. In Fig. 1-1c, the elliptical conductor touches the polarized conductor and some of the negative charge transfers to the elliptical conductor due to repulsive force from the negative charged object. In Fig. 1-1d, the elliptical conductor is removed, taking some negative charge with it and leaving a net positive charge on the round conductor. In Fig. 1-1e, the negatively charged object has been removed. The charge on the round conductor re-distributes, but the overall charge on the conductor is now positive. Note that we have ignored polarization of the elliptical conductor.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
3
Fig. 1-1: Charging sequence.
Setup A
1.
Connect the Electrometer to the Faraday Ice Pail as shown in Fig. 1-2. Connect the alligator clip with the red band to the inner conductor and the ground (black alligator) to the outside conductor. The Electrometer is a device that can measure the voltage difference between small charges without affecting the charges. When a charge Q
is placed inside the inner cylinder, the cylinder becomes polarized with a charge almost (exact if there was not an open top) equal to Q
moving to the outside of the inner cylinder. The voltage between the inner and outer cylinders is directly proportional to charge on the outside of the inner conductor, so this gives a way to directly measure the change inside the “ice pail”. Fig. 1-2: Charging setup.
2.
Turn on the Electrometer and set the range to 10 V. 3.
Ground the ice pail by touching a finger to both the inner and outer cylinder at the same time. Then remove the finger from the inner cylinder and then the finger from the outer cylinder as showed in Fig. 1-3. The word “grounding” is used to mean removing all (really just most of) the
4
excess charge. We generally do this by touching the system with a conductor that is much larger than the system, in this case our bodies.
Fig. 1-3: Grounding the Ice Pail.
4.
Press the “ZERO” button on the electrometer. This forces the electrometer to read zero even if there is a charge on the ice pail. This is okay since we really are only interested in changes
in the charge.
5.
You may need to redo the grounding and/or zeroing of the ice pail during the experiment. It is very easy to transfer charge to the ice pail by touching it or even getting too close to it with a charged object. 6.
Change the Range on the electrometer to 100 V. Press the Zero button again.
7.
One at a time, insert the disks on the Charge Producer wands (one with a dark plastic disk and the other with a white leather disk) into the inner basket. Where are your hands? If the disks are uncharged, the needle in the electrometer will stay at zero. If the needle moves, then there is residual charge in the wands. To remove the residual charge, touch the charge producers to the outer basket of the grounded ice pail. Sometimes if residual charge is hard to remove, you can breathe on the disks. The moisture from your breath will remove the charges. It is difficult to remove all the charge since the disks are non-conducting. If you see a voltage change of less than one volt, that is good enough. Procedure A1: Charging by Rubbing Objects Together. 1.
Ground the ice pail, zero the electrometer and make sure there is no charge on the charge producing wands (see step 7 under Setup A). 2.
Hold one wand in each hand and lower them into the lower half of the inner basket, without
5
letting them touch each other or the walls of the basket (Fig. 1-4). Since there is no net charge in either wand, the needle in the monitor should not move and still read nearly zero. Press the Zero button on the electrometer. Record the “initial” reading in row 1 of Table I.
Fig. 1-4: Charging procedure.
Table I: Electrometer Voltages
Reading
Run 1
(V)
Run 2
(V)
Run 3
(V)
1
Initial
2
After rub
3
After separation
4
Dark out
5
Both in
6
White out
7
Final
8
Both out
9
Sum
3.
Do all of the following steps as rapidly as possible to minimize charge migration to the surroundings.
4.
While inside the basket, briskly rub the two charge producers together and observe the needle in the monitor. Record the “after rubbing” reading in row 2 of Table I.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
6
5.
Stop rubbing. Still inside the basket, separate the wands and observe the needle in the monitor. Record the “after separation” reading in row 3 of Table I.
6.
Take the dark wand out of the basket. Record the “dark out” reading in row 4 of Table I.
7.
Insert the dark wand into the basket with the white wand (not touching). Record the “both in” reading in row 5 of Table I.
8.
Remove the white wand. Record the “white out” reading in row 6 of Table I.
9.
Insert the white wand into the basket with the dark wand. Record the “final” reading in row 7 of Table I.
10.
Remove both wands. Record the “both out” reading in row 8 of Table I.
11.
Rub the two wands together and then remove the charge from the white one by touching it to the outside mesh cylinder. Ground the ice pail with your finger and zero the electrometer. Repeat steps 2-10.
12.
Rub the two wands together and then remove the charge from the black one. Ground the ice pail and zero the electrometer. Repeat steps 2-10.
Analysis A1
1.
What can you immediately conclude about the charges on the white wand and the dark wand based on the signs of the voltages in Run 1?
2.
Note that lines 3, 5, and 7 are exactly the same system so should have the same voltage. Any difference implies that there has been some charge lost or gained. In addition, line 8 should be zero unless some charge has transferred. Looking at these should allow you to estimate the uncertainties in the experiment and decide if numbers agree within the uncertainties.
3.
Recall that the voltage is directly proportional to the charge. Thus if a voltage of 8 V implies 8 units of charge, a voltage of 12 V implies 12 units of charge.
4.
What do lines 1-3 imply?
5.
Add line 4 to line 6 (do not forget the sign). Enter the sum on line 9.
6.
Compare line 1 to line 9. What does this imply?
7
Procedure A2: Charging by Contact. 1.
Ground the ice pail and zero the electrometer. Record the "zero" reading in line 1 of Table II.
2.
Briskly rub the white and dark charge producers together to charge them.
3.
Insert the white charge producer into the inner basket of the ice pail. Record the “initial” voltage on the electrometer in line 2 of Table II. 4.
Let the white disk on the charge producer touch the wall of the basket. Record the “after touch” voltage on the electrometer in line 3 of Table II.
5.
Remove the white disk. Record the “disk out” voltage on the electrometer in line 4 of Table II.
6.
Repeat steps 1-5 using the dark charging disk.
Procedure A3: Charging by Induction 1.
Ground the ice pail and zero the electrometer. Record the "zero" reading in line 1 of the Charge by Induction in Table II.
Table II: Charge by Contact/Induction
State
White Disk
Contact
(V)
Dark Disk
Contact
(V)
White Disk
Induction
(V)
Dark Disk
Induction
(V)
1
Zero
2
Initial
3
After touch
4
Disk out
2.
Rub the wands together to charge them.
3.
Without letting the wand touch the ice pail, insert the white wand into the lower half of the inner basket. Record the “initial” voltage on the electrometer in line 2 of Table II.
4.
While the charge producer is inside the basket, momentarily ground the ice pail by bridging between the outer and the inner cylinder with your finger and then removing your finger. Record
8
the “after touch” voltage on the electrometer in line 3 of Table II.
5.
Remove the wand from the ice pail. Record the “wand out” voltage on the electrometer in line 4 of Table II.
6.
Repeat steps 1-5 using the dark charge producer.
Analysis A2/A3
1.
What can you conclude from the data in the 2
nd
and 3
rd
columns (contact data) in the table?
2.
Explain what is happening when you induce a charge on the inner mesh cylinder. That is, explain the data in columns 3 & 4 of the table. Why does the sign change?
B – Distribution of Charge
Theory B
Charge Distribution on a Conducting Surface: Charge will tend to concentrate at places on a conductor where the surface is more sharply curved. This happens because charges do not interact as strongly with other charges that are “over the horizon” since the electric field lines cannot pass through a conductor.
Charge inside a Spherical Conducting Shell: If the force between two point charges obeys an inverse square law
(i.e. falls off like 1/r
2
), then all the charge on a conducting spherical shell must lie on the outside of the shell and the inside of the shell must be uncharged. Although we check this crudely here, it is possible to verify this with great precision and it is currently known that the exponent is 2 to within better than 1 part in 10
30
! Procedure B1: Measuring the Charge at Different Locations on the Outer Surface of a Spherical Conductor
1.
Plug in the Electrostatics Voltage Source and turn it on. Attach a black lead from the Common (Com) jack to the ground port in the Electrometer. Attach the red lead to the +3000 V terminal and leave the spade connector on one end of the red lead unattached.
P.S. You cannot get shocked by this power supply since it can only produce a tiny current.
2.
Ground the ice pail (the inner cylindrical wire mesh) with your finger as before. Turn on the electrometer, set it to the 30 V range, and zero the electrometer.
3.
The “proof plane” is the metal disk (silver looking) on one of the black wands. It is used for
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
9
sampling charge on a conductor by touching it to the surface of the conductor. The amount of charge that transfers to the proof plane is proportional to the surface charge density at the point of contact. Make sure there is no charge in the proof plane by inserting it into the inner mesh cylinder. The electrometer should read zero. If there is charge on the proof plane ground it by touching it to any ground or the outer mesh cylinder.
4.
Place the spherical conductor (no hole) well away from other objects (including people) to prevent polarization effects. Nothing should be closer to the sphere than the base on which it sits. The Faraday Ice Pail should also be well away from the sphere. You should perform the following steps as rapidly as possible to prevent significant discharge of the sphere though the air.
5.
Connect the red lead (the spade lug) to the thumbscrew on the conductive sphere (without a hole), as in Fig. 1-5. This will charge the conductor to an electric potential of 3000 V. Fig. 1-5: Conductive sphere setup.
6.
Touch the sphere at point A (see Fig. 1-6) with the proof plane keeping your hands as far away as possible. Place the proof plane so that it is tangent to the surface of the conductive sphere, Fig. 1-7.
10
Fig. 1-6: Charge distribution on a sphere.
Fig. 1-7: Using a proof plane to sample charge.
7.
Put the proof plane in the inner cylinder of the ice pail and record the voltage from the electrometer on Fig. 1-6 at point A. Do not ground the proof plane so the total charge on the sphere and proof plane remains constant.
8.
Repeat for points B & C.
Analysis B1
Recall that the voltages recorded on Fig. 1-6 are not the voltages on the sphere (the sphere is at a uniform 3000 V). They are the voltages between the inner and outer mesh cylinders with the proof plane inside the inner cylinder, which is directly proportional to the charge on the proof plane. What can you conclude about the distribution of charge on the sphere?
11
Procedure B2: Charging the Spherical Conductor to Different Potentials
1.
Same setup as in Procedure B1.
2.
Ground the ice pail. Set the electrometer to the 10 V range and zero the electrometer. Make sure there is no charge in the proof plane. The electrometer should read zero. Repeat this anytime the electrometer does not read zero with nothing in the ice pail. 3.
With one end of the red lead in the +1000 V terminal of the Electrostatics Voltage Source, connect it to the surface of the conducting sphere.
4.
Touch the top of the sphere with the proof plane.
5.
Without letting it touch the basket, insert the proof plane into the lower half of the inner basket of the ice pail. Record the electrometer voltage in the second column of Table III.
Table III: Voltage vs. Charge on a Sphere
Sphere Potential
(V)
Electrometer Reading
(V)
1000
2000
3000
6.
Ground the proof plane. Make sure there is no residual charge in the proof plane before continuing.
7.
Repeat the measurement for the +2000 V and +3000 V outputs (still on the 10 V range). If the reading is 9.9 V, you have exceeded the range. In that case, change the electrometer to the 30 V range, ground the ice pail, zero the electrometer, and proceed.
Analysis B2
Recall that the electrometer voltages are the voltages between the inner and outer mesh cylinders with the proof plane inside the inner cylinder, which is directly proportional to the charge on the proof plane. What can you conclude about the charge on the sphere vs the electric potential (voltage) of the sphere?
Procedure B3: Measuring the Charge on the Outer Surface of a Non-Spherical Conductor
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
12
1.
Same setup as Procedure B1, except replace the sphere with the non-spherical conductor. Use the +3000 V terminal on the Voltage Source. Electrometer on the 30 V range.
2.
Ground the ice pail, zero the electrometer and make sure there is no charge in the proof plane. The electrometer should read zero.
3.
Briefly connect the oblong-shaped conductor to the +3000 V outlet of the Electrostatics Voltage Source.
4.
Touch the large-radius end (point A in Fig. 1-8) of the oblong shaped conductor with the proof plane.
5.
Without letting it touch the basket, insert the proof plane into the lower half of the inner basket of the ice pail. Record the reading from the electrometer on Fig. 1-8 at point A.
6.
Repeat the process at points B & C. Do not ground the proof plane so the total charge remains constant.
Fig. 1-8: Non-spherical charge distribution.
Analysis B3
What can you conclude about the distribution of charge on a non-spherical conductor?
Procedure B4: Measuring the Charge on the Inner Surface of a Spherical Conductor
1.
Same setup as Procedure B3 except replace the oblong conductor with the sphere with a hole on top.
13
2.
Ground the ice pail, zero the electrometer and make sure there is no charge on the proof-plane wand. You need to make a decision here. You may use either the disk end of the proof plane or the ball end. The ball end was designed for this experiment. However, it picks up a smaller amount of charge than the disk does, so requires you to operate on the 3 V range of the electrometer. The problem is that it is very easy to charge the non-conducting parts of the wand and on the 3 V range; these charges have a large impact, and it is very difficult to discharge them. If you can successfully ground the ball end so that the electrometer remains near zero when the uncharged ball is inserted in the inner cylinder, then the ball works fine. If not, use the disk with the electrometer on the 30 V range. Little charges on the handle are then not so important. However, considerable care is required to insert the disk into the hole without touching the sphere, and there is a risk of charge transfer even if the disk just comes close to the edge of the hole without touching.
3.
Briefly touch the end of the red lead (attached to the +3000 V terminal) to the conducting sphere. 4.
Keeping the proof plane as far as possible from the edges of the hole, insert the uncharged proof plane into the charged sphere and touch the inner wall near the bottom. Remove the proof plane from the hole. If the proof plane touches the edge, start over.
5.
Without letting it touch the basket, insert the proof plane into the lower half of the inner basket of the ice pail. Record the electrometer reading in the first line of Table IV.
Table IV: Sphere Voltages
Sphere with Hole
Electrometer Voltage
(V)
1
Inside
2
Inside near hole
3
Outside
4
Inside again
5
Outside again
6.
Keeping the proof plane as far as possible from the edges of the hole, insert the uncharged proof plane into the charged sphere and touch the inner wall near the hole. Be careful that the wand does not touch the edge of the hole or you will put a charge on the wand. Remove the proof plane from the hole. If the proof plane touches the edge, start over.
7.
Without letting it touch the basket, insert the proof plane into the lower half of the inner basket
14
of the ice pail. Record the electrometer reading in the second line of Table IV.
8.
Touch the proof plane to the outside of the sphere (anywhere) and repeat step 7, recording the value from the electrometer on line 3.
9.
Without grounding it, insert the proof plane in the hole and touch the inner wall near the bottom. Repeat step 7, recording the value on line 4.
10.
Touch the proof plane to the outside of the sphere (anywhere) and repeat step 7, recording the value from the electrometer on line 5. If lines 3 and 5 are nearly equal and around 10 V, your data is probably OK. Variations of ± 1 V are probably not significant.
Analysis B4
1.
What does the data in the table tell you about the distribution of charge on a hollow spherical shell?
2.
Explain what happened in line 4 of Table IV.
Questions for Your Lab Report
In addition to questions posed in this section, answer the following questions in your lab report.
Note:
The answers to the fill-in-the-blanks questions are about the registers polarity of the electrometer. Answer ‘Positive,’ ‘Negative,’ or ‘Zero.’
OBSERVATIONS PROCEDURE A: Charging by Rubbing Objects Together
While rubbing the two charge producers together inside the basket:
The charge detected is __________.
After rubbing, with wands still in the basket, but not touching:
The charge detected is __________.
After removing the dark wand from the basket:
The charge detected on the white wand alone is __________.
The charge detected on the dark wand alone is __________.
QUESTIONS PROCEDURE A:
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
15
1.
While the two wands were being rubbed against each other, what was their overall net charge?
2.
After the rubbing process, what was the net overall charge of the two wands?
3.
What is the evidence that the rubbing process gave each wand an electric charge?
4.
What is the polarity of the white charge producer after rubbing it with the dark one? Did the white wand gain or did it lose electrons during the rubbing process? Where did the electrons go (or come from)?
5.
What is the polarity of the dark charge producer after rubbing with the white one? Did the dark wand gain or did it lose electrons during the rubbing process? Where did the electrons go (or come from)?
6.
Explain how this experiment demonstrates the law of conservation of charge.
OBSERVATIONS PROCEDURE B:
Charging by Contact
After placing the white charge producer in the inner basket:
The charge detected is ___________________.
After letting the charge producer touch the wall of the basket:
The charge detected is ___________________.
After inserting the dark charge producer into the inner basket and letting it touch the basket: The charge detected is ___________________.
QUESTIONS PROCEDURE B:
1.
Before the white wand touched the basket, what was the polarity of the white wand? What was the state of the basket?
2.
After the white wand touched the basket, what was the polarity of the basket? Did the basket gain or lose electrons during the contact with the white wand? Where did the electrons go (or come from)?
3.
After the dark wand touched the basket, what was the polarity of the basket? Did the basket gain or lose electrons during the contact with the dark wand? Where did the electrons go (or come from)?
4.
When a charged object touches an initially neutral object, the neutral object acquires a charge. How does the polarity acquired by the initially neutral object compare to the polarity of the charged object that touched it?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
16
OBSERVATIONS PROCEDURE C:
Charging by Induction Without letting the wand touch the ice pail:
The polarity of the charge on the white wand is _________________.
After grounding the ice pail and removing the wand:
The polarity of the charge on the pail is ___________________.
Repetition with the dark charge producer:
The polarity of the charge on the dark wand is _________________.
After grounding, the polarity of the charge on the pail is _______________.
QUESTIONS PROCEDURE C:
1.
At the end of the process, how does the charge acquired by the pail compare to the polarity of the charge on the wand that was used?
2.
When using the white wand, did the ice pail gain or lose electrons during the charging by induction process? Where did the electrons go (or come from)?
3.
When using the dark wand, did the ice pail gain or lose electrons during the charging by induction process? Where did the electrons go (or come from)?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
17
Experiment 1.2 −
Capacitance
Equipment
1
Basic Electrometer
ES-9078
1
Basic Variable Capacitor
ES-9079
1
Electrostatics Voltage Source
ES-9077
Paper
Introduction
The purpose of this experiment is to investigate how the capacitance of a parallel-plate capacitor varies when the plate separation is changed and to qualitatively observe the effect of introducing a dielectric material between the plates. A computer model of the system will be developed and the student will observe some of the power of computer modeling.
Theory
A capacitor is used to store charge. A capacitor can be made with any two conductors kept insulated from each other. If the conductors are connected to a potential difference, V
, as in for example the opposite terminals of a battery, then the two conductors are charged with equal but opposite amount of charge Q
, which is then referred to as the “charge in the capacitor.” The actual net charge on the capacitor is zero. The capacitance of the device is defined as the amount of charge Q
stored in each conductor after a potential difference V
is applied:
? = ?/?
Rearranging gives: ? = ?/?
(1)
The simplest form of a capacitor consists of two parallel conducting plates, each with area A, separated by a distance d (Fig. 1-9). The charge is uniformly distributed on the surface of the plates. The capacitance of the parallel-plate capacitor is given by:
Fig. 1-9: Parallel-plate capacitor.
? = 𝜖
?
𝜖
?
?/?
where 𝜖
?
is the dielectric constant of the insulating material between the plates (
𝜖
?
= 1
for a vacuum; other values are measured experimentally and can be found in tables), and 𝜖
?
is the permittivity constant, of universal value 𝜖
?
= 8.854 × 10
−12
F/m. The SI unit of capacitance is the Farad (F).
The system we use is more complex. In addition to the two moveable parallel plates, the connecting wires and the electrometer also have some capacitance. This capacitance is roughly equal to the capacitance of the moveable plates when the plates are 1 cm apart and cannot be ignored. Including
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
18
this gives:
? = 𝜖
?
𝜖
?
?/? + ?
???
(2)
where ?
???
is the capacitance of the rest of the system. Substitution of Equation 2 into Equation 1 yields:
? = ?/(𝜖
?
𝜖
?
?/? + ?
???
)
(3)
Any material placed between the plates of a capacitor will increase its capacitance by a factor 𝜖
?
called the dielectric constant where:
? = 𝜖
?
?
?
(4)
with ?
?
being the capacitance when there is a vacuum between the plates of the capacitor.
Dielectric materials are non-conductive. Any dielectric material can be used to keep the plates in a capacitor insulated from each other (preventing them from touching and discharging). To three significant figures, 𝜖
?
= 1.00
for air. For all materials, 𝜖
?
> 1
. If the charge on a capacitor is kept constant while a dielectric is inserted between the plates, Equations 1 & 4 yield:
? = ?? = ?
?
?
?
= (? 𝜖
?
⁄
)?
?
so ? = ?
?
/𝜖
?
where ?
?
is the voltage before inserting the dielectric and V is the voltage after insertion. Since 𝜖
?
> 1
always, we have ? < ?
?
.
(5)
Setup
1.
Move the Variable Capacitor plates so they are about 0.2 cm apart. Use the adjustment screws on the back of the moveable plate to make the plates parallel. Easiest way to do this is to look directly down from above the plates and adjust the horizontal adjust until the gap looks uniform, then look at the gap from the side, even with the center of the plates, and adjust the vertical screw. You may need to repeat the process a few times.
2.
Position the movable plate so that the leading edge of the indicator foot (see Fig. 1-10) is at the 0.2 cm position. The gap between the two plates should be 0.2 cm all the way around. Check it with a ruler. If the gap varies repeat step 1. If the gap is not 0.2 cm, release the holding screw on the non-moving plate and move it until the gap is 0.2 cm and then tighten the screw back down.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
19
Fig. 1-10: Indicator foot.
3.
Attach the twin lead (red & black) connector to the Signal Input jack on the Basic Electrometer. Route the wires as far away from where your hand and your body will be as possible. The charges in this experiment are all small, so static discharge will result in measurement errors. Also, people are conducting plates and have a significant amount of capacitance. You can introduce measurement errors just by being close
. It is best to make the fixed plate ground by attaching the black wire’s spade lug to it. Attach the red spade lug to the terminal on the moving plate. The wire must be free to move when the plate moves (Fig. 1-10).
Fig. 1-10: Setup.
4.
Attach a black banana wire as shown from the common (com) terminal on the Electrostatic Voltage Source to the ground terminal on the Electrometer. Alternately, use the spade wire and connect the spade lead to the terminal on the fixed plate where the other ground lead is already attached. Attach the red spade lead to the +30 V terminal and leave the spade end free. Plug in the transformer and apply power to the Electrostatic Voltage Source. Shift the switch on the back to the On position. The green Power On light should glow.
5.
Open Pasco Capstone, select Table & Graph to create a table as shown in Table V and Table VI, and enter the values of the voltage measurement in the second column. 6.
Create a graph of Voltage vs. Separation.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
20
Table V: Air Gap Capacitor – RUN 1
Table VI: Air Gap Capacitor – RUN 2
Separation (cm)
Voltage (V)
0.3
0.5
1.0
1.5
2.0
3.0
4.0
5.0
Separation (cm)
Voltage (V)
5.0
4.0
3.0
2.0
1.5
1.0
0.5
0.3
Procedure A: The Effect of the Plate Separation
1.
Set the capacitor plates 0.3 cm apart by setting the movable plate so that the leading edge of its indicator foot is at the 0.3 cm mark.
2.
Turn on the electrometer and set the range button to the 100 V scale.
3.
Remove any charge from the capacitor by momentarily touching both plates at the same time with your hand.
4.
Zero the electrometer by pressing the ‘ZERO’ button until the needle goes to zero.
5.
Momentarily connect a cable from the +30 V outlet in the voltage source to the stud on the back of the movable capacitor plate. This will charge the capacitor. Remove the charging cable.
6.
Read the following steps. They need to be performed quickly since the charge will slowly escape from the electrometer, especially if the humidity is high. One person should run the computer while one moves the capacitor plate. Everyone else should stay back. Everyone should try to be in the same position for each reading. Anybody who is close is a significant part of the system and can make the readings change.
7.
Slide the movable plate so it is at 5.0 cm (leading edge of the indicator foot). Once the plate is in position, the person moving the plate should move away 50 cm or so and try to be in the same position for each measurement. 8.
Move the plate to 5.0 cm and repeat the process until 0.3 cm.
Analysis A
? = ?/(𝜖
?
𝜖
?
?/? + ?
???
)
(3)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
21
Examination of Equation 3 from Theory A show that if ?
???
= 0
, then ?
is directly proportional to ?
and the Voltage vs. Separation graph should be a straight line. This is clearly not the case. To verify Equation 3 for the case where ?
???
is not zero, we need to know ?
and ?
???
. We determine these by fitting the math model (Equation 3) to the data.
First we note that 𝜖
?
𝜖
?
? = (1.00)(8.85 × 10
−12
F m
⁄
)(2.46 × 10
−2
m
2
) = 2.18 × 10
−13
Fm = 2.18 × 10
−11
F ∙ cm
So the parallel plate capacitance, when ? = 1
cm, is ?
1.0
= 2.18 × 10
−11
F. Note that this value is entered in line 2 of the Calculator.
When ?
is small (0.3 cm) the first term in the denominator dominates and ? ≈ ?
0.3
(𝜖
?
𝜖
0
?)
?
⁄
= (30 V) × (2.18 × 10
−11
F ∙ cm)
(0.3 cm)
⁄
= 2.2 × 10
−9
C
This value is entered as an initial guess for the value of ?
in line 1 of the calculator. ?
is constant so when d becomes large, ?
???
dominates in the denominator and we have:
?
???
≈ ? ?
8
⁄
≈ 2.2 × 10
−9
C
80 V
⁄
= 2.7 × 10
−11
F
where ?
8
is the voltage when ? = 8
cm. This is taken as the initial guess for ?
???
(= ?
1
)
on line 3 of the calculator. Note that ?
???
is about equal to ?
1.0
at 1.0 cm. At 0.3 cm, ?
0.3
= 7 × 10
−11
F so ?
0.3
≈ 3 ?
???
and the approximation above is decent but not great. At 8 cm, ?
8
= 2.7 × 10
−12
F = ?
???
10
⁄
, so the approximation is good, but not perfect.
1.
In the calculator , create the following calculations:
?
= 3.0e-9
Units of C
𝜖
?
𝜖
?
?
= 2.18e-11
Units of (F cm)
?₁
= 3.6e-11
Units of F
?
model = [
?
]/([
𝜖
?
𝜖
?
?
]/[Separation]+[
?₁
]) Units of V
2.
Create a Graph to compare the data measured with the model from Equation 3.
3.
Adjust the values for ?
on line 1 and for ?
1
on line 2 to make the model match the experimental curve as well as possible.
4.
Answer the first four questions on the conclusions page.
Procedure B: The Effect of a Dielectric Between the Plates
1.
You will use paper as the dielectric to be inserted between the plates. Get a stack of paper about 1 cm thick.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
22
2.
Position the movable plate of the capacitor at 7 cm.
3.
Turn on the electrometer and set the range button to the 100 V scale.
4.
Remove any charge from the capacitor by momentarily touching both plates at the same time with your hand.
5.
Zero the electrometer by pressing the ‘ZERO’ button. The needle must be at zero.
6.
Momentarily connect a cable from the +30 V outlet in the voltage source to the stud on the back of the movable capacitor plate. This will charge the capacitor. Remove the charging cable.
7.
One student holds the stack of paper directly above the gap between the capacitor plates so that the long side of the paper is vertical. Hold the paper with one hand and keep the other hand on the metal connector attached to the signal input of the Electrometer so that there is no static charge on the student holding the paper. 8.
Lower the paper between the two plates until it touches the base. Do not let the paper touch either plate! Keep your hand as far above the plates as possible. Record the voltage when the paper is between the plates.
9.
Pull the paper back above the plates and repeat steps 7 and 8 several times.
10.
Write the values of the voltage down in Table VII for the following conditions. Table VII: Paper Dielectric
Paper
Position
Voltage
(V)
1
out
2
in
3
out
4
in
5
out
6
in
Conclusions
1.
What happened to the voltage as the plates got closer together (d decreasing)? 2.
What were your best fit values for the charge ?
and C
sys
?
3.
How well did your model fit the data? Try to explain any discrepancy. Hint: What approximations are made when deriving the parallel plate capacitance (
? = 𝜖
?
𝜖
?
?/?
)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
23
from Gauss’ Law?
4.
Briefly discuss the value of computer modeling. 5.
Examine Table VI. Does the data agree with Equation 5? What does a dielectric do?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
24
E
XPERIMENT 2
—
M
AGNETIC F
IELDS OF C
OILS
Equipment
Helmholtz Coil Base
EM-6715
Field Coil (500-Turn)
EM-6723
Primary and Secondary Coils
SE-8653A
Patch Cords (set of 5)
SE-9750
Patch Cords (set of 5)
SE-9751
60 cm Optics Bench
OS-8541
Dynamics Track Mount CI-6692
20 g hooked mass (Hooked Mass Set)
SE-8759
Small Round Base (Set of 2)
ME-8974A
25 cm Steel Rod
ME-8988
Optics Bench Rod Clamps (Set of 2)
OS-8479
2-Axis Magnetic Field Sensor
PS-2162
Rotary Motion Sensor
PS-2120
Zero Gauss Chamber
EM-8652
Introduction
The magnetic fields of various coils are plotted versus position as the Magnetic Field Sensor is passed through the coils, guided by a track. The position is recorded by a string attached to the Magnetic Field Sensor that passes over the Rotary Motion Sensor pulley to a hanging mass.
It is particularly interesting to compare the field from Helmholtz coils at the proper separation of the coil radius to the field from coils separated at less than or more than the coil radius. The magnetic field inside a solenoid can be examined in both the radial and axial directions.
Theory
Single Coil
For a coil of wire having radius R (Fig. 2-1) and N turns of wire, the magnetic flux density along the perpendicular axis through the center of the coil is given by
? = 𝜇
0
𝑁𝐼𝑅
2
2(?
2
+𝑅
2
)
3
2
⁄
(1)
Fig. 2-1: Single coil.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
25
Two Coils
For two coils, the total magnetic flux density is the sum of the magnetic flux densities from each of the coils. On the axis we have:
? = ?
1
+ ?
2
? = 𝜇
0
𝑁𝐼𝑅
2
2
1
((?−? 2
⁄ )
2
+R
2
)
3
2
⁄
+((?+? 2
⁄ )
2
+R
2
)
3
2
⁄
(2)
where 𝑥
is measured from the geometric center as shown in Fig. 2-2.
Fig. 2-2: Two coils with arbitrary separation (left) and Helmholtz coils (right).
For Helmholtz coils, the coil separation (d) equals the radius (R) of the coils. This coil separation gives a uniform magnetic field between the coils. Plugging in 𝑥
= 0 gives the magnetic field at a point on the 𝑥
-axis centered between the two coils:
?
⃗ = 8𝜇
0
𝑁𝐼
√125
𝑅
𝑥
̂
(3)
Solenoid
For a long solenoid with n turns per unit length (Fig. 2-3), the magnetic flux density is ? = 𝜇
0
?𝐼
.
(4)
The direction of the field is straight down the axis of the solenoid.
Fig. 2-3: Solenoid.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
26
Setup
1.
Attach a single coil to the Helmholtz Base so it is aligned with the white rectangle on the base and thus perpendicular to the base. Connect a DC power supply across the coil as shown in Fig. 2-4. Also, connect an ammeter to measure the current through the coil.
Fig. 2-4: Setup – Single coil.
2.
Pass the optics track through the coil and support the two ends of the track with the support rods. One end of the optics track should be close to the edge of the table so when you hang a mass over the Rotary Motion Sensor, it will hang freely over the edge of the table.
3.
Level the track and adjust the height so the Magnetic Field Sensor probe will pass through the center of the coil when it is pushed along the surface of the track against the side with the yellow metric scale. An accurate way to do this is shown in Fig. 2-5. The coil diameter is 23.4 cm. The height is adjusted (while maintaining level) so that a thin metric ruler lies just below the holes in the side of the coil holder, and 0 cm is at the edge of the coil. The track is adjusted so that the white dot marking the axial sensor is at the 11.7 cm mark. The bottom of the sensor probe is even with the ruler. The coil base needs to be parallel with the optics track. Note that the coil is 2 cm wide, so the exact coil center is 1 cm from the edge of the ruler (at 17 cm in Fig. 2-5). When the white dot on the side of the magnetic probe is at this point (17 cm on the yellow scale in Fig. 2-5), the sensor is very close to the coil center.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
27
Fig. 2-5: Finding the coil center.
4.
Attach the Rotary Motion Sensor to the track using the bracket as in Fig. 2-6. Cut a piece of thread long enough to reach from the floor to the track. Tie a loop in one end of the thread and slide the sensor probe of the Magnetic Field Sensor through it (see Fig. 2-5). Pass the other end of the thread over the middle step of the Rotary Motion Sensor pulley and attach the 20-g mass. Place the Magnetic Field Sensor against the side of the track with the yellow scale and adjust the position of the Rotary Motion Sensor so the thread is aligned with the middle step pulley. 5
Fig. 2-6: RMS setup.
5.
Turn on the wireless sensors. In PASCO Capstone, connect wirelessly to the Wireless Rotary Motion sensor and the Wireless 3-Axis Magnetic Field sensor. Keep the default sample rate of 20 Hz.
6.
Create a graph of Axial Magnetic Flux Density (T) vs. Position (cm) and another one of the Perpendicular Magnetic Flux Density (T) vs. Position (cm). Note: Keep the unit for Magnetic Flux Density in Tesla (T) and Position in centimeter cm.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
28
Single Coil Procedure
1.
Find the radius of the coil by measuring the diameter from the center of the windings on one side across to the center of the windings on the other side. Enter the value in the Coil Properties table in the Analysis 1 section.
2.
To zero the Magnetic Field sensor, insert the probe into the Zero Gauss Chamber. You must make sure that the Magnetic Field sensor is selected in the sample rate window. Looking at the X-Magnetic Flux Density vs. Time graph, start recording, and in the properties of the sensor, click in “Zero Sensor Now”, Fig. 2-7. Make sure that the sensor reads zero. If not, click the zero button again.
Then stop recording and delete the last run.
Fig. 2-7: Zero Gauss Chamber (left) and 3-axis magnetic field properties (right).
3.
Slide the Magnetic Field Sensor along the track until the probe sensor is in the middle of the coil. Open the properties of the Rotary Motion Sensor and click on “Zero Sensor Now”, Fig. 2-8. This will make zero on the 𝑥
-axis be at the center of the coil. The motion sensor has an orientation of scrolling, which can show a positive or negative position. Also, select the pulley you will be using.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
29
Fig.2- 8: RMS properties.
4.
In the power supply, set the voltage to 15 V.
5.
Start sliding the Magnetic Field Sensor in the position of 15 cm away from the coil. Click RECORD and slowly move the Magnetic Field Sensor along the track, keeping it against the side with the yellow scale, until the end of the sensor is about 15 cm past the coil. Then click STOP.
6.
Record the Coil Current from the Ammeter. 7.
In the calculator, write the Equation 1. Type m as symbol for
0
. Enter m = 1.257e-6, the current, the coil radius, number of turns in the coil and coil distance, on axis. Create a graph for the theoretical from the calculation. Analysis 1: Single Coil
Discuss any differences between the experimental axial curve and the theoretical fit.
The perpendicular flux density should be zero everywhere on the axis. If it is not, why not? Helmholtz Coil Setup
1.
Attach a second coil to the Helmholtz Base at a distance from the other coil equal to the radius of the coil. Note that you cannot just use the white rectangles on the base since it was designed for the 200 turn coils and the 500 turn coils have a slightly larger diameter.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
30
Make sure the coils are parallel to each other (the white rectangles do help, Fig. 2-9). The left coil is about 15 cm from the end of the track. Align coils & track as before.
Fig. 2-9: Helmholtz coil setup.
2.
Connect the second coil in series with the first coil. See Fig. 2-9 and Fig. 2-10. Note that the connectors on the coil all face outward and that the black jumper cable between the coils goes from black connector to black connector. The other black cable goes from the white connector to the black connector on the DC power supply. Fig. 2-10: Helmholtz wiring.
3.
Slide the magnetic field sensor along the track until the end of the Magnetic Field Sensor in the halfway between the two coils. Open the properties of the Rotary Motion Sensor in the Data Summary and click on "Zero Sensor Now". This will make zero on the 𝑥
-axis be at the center between the coils. "Zero on Start" should still be unchecked.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
31
Helmholtz Coil Procedure
1.
Slide the Magnetic Field Sensor back away from the coils until it is about 15 cm from the first coil. Turn on the power supply (15 V). Start recording and slowly move the Magnetic Field Sensor along the center of the track, keeping the probe parallel to the track, until the end of the sensor is about 15 cm past the second coil. Then stop recording.
2.
Create the following calculations:
Btheory = 0.5𝜇
?
?𝐼?
2
(([???𝑖?𝑖??] − ? 2
⁄ )
2
+ ?
2
)
−1.5
+ (([???𝑖?𝑖??] + ? 2
⁄ )
2
+ ?
2
)
−1.5
Units of T
μ
₀
=[Permeability constant]
Units of Tm/A
I= [Measured]
Units of A
R=0.105
Units of m
d=0.105
Units of m
3.
Create a graph for the Btheory from the calculation.
4.
Does the theoretical equation fit everywhere? If not, why not?
Two Coils Not at Helmholtz Spacing
1.
Now change the separation between the coils to 1.5 times the radius of the coils. Add a new page and repeat the scan. Label this run "1.5 R". 2.
Now change the separation between the coils to half the radius of the coils. Repeat the scan. Label this run "0.5 R". 3.
How does changing the coil spacing affect the magnetic field?
Solenoid Procedure
1.
Setup as shown in Fig. 2-11 by setting the solenoid on the optics track. Note that the magnetic sensor probe goes just past halfway through the coil when fully inserted. The Magnetic Field sensor is still connected to the Rotary Motion Sensor.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
32
Fig. 2-11: Solenoid Setup
2.
Connect the DC power supply to the solenoid. Add the multimeter to measure Voltage and Current.
3.
With the DC power off, put the Magnetic Field Sensor all the way inside the solenoid, zero the sensor. Click Rotary Motion Sensor properties and click “Zero Sensor Now”. Note the position of the solenoid on the track and try not to move it during the rest of the experiment. 4.
Set for a Voltage of 10 V. Click the DC Voltage on. Click RECORD and adjust the DC Voltage until the Solenoid Current reads about 100 mA. Click STOP. 5.
Click RECORD. Move the sensor around inside the solenoid staying within a few cm of the center, but moving from the axis to the edge of the coils and back. Click STOP. 6.
Examine the Central Field graph. Is the field inside the solenoid the same everywhere? 7.
Measure the length of the coil (between the end blocks). PASCO specs list the coil as having 2920 turns. Using this information and Equation 4 from Theory, calculate the theoretical value of the magnetic flux density. Click on the black triangle by the Statistics icon and select “mean”. Click on the Statistics icon. The mean value should appear on the left of the graph. Compare this value to the theory value. Solenoid Field
1.
Insert the magnetic sensor probe fully into the solenoid.
2.
Click RECORD. Move the probe slowly out of the solenoid and about 5 cm beyond. Click STOP.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
33
3.
Note that the sensor is about 7 cm from the body of the Magnetic Field Sensor, so the sensor exits the coil when the position is about 7 cm.
4.
Is the perpendicular field equal to zero?
5.
What happens to the axial field as you approach the ends of the coil?
6.
Does the field go to zero outside the coil?
Magnetic Field across a Single Coil
1.
Set up the single coil as before except instead of putting the track through the coil, set up the track so it is parallel to the face of the coil. Make sure the elevation of the track is set so the magnetic probe is at the height of the center of the coil.
2.
Create a graph of the Axial Magnetic Flux Density vs. Position and then add a second plot area for the Perpendicular Magnetic Flux Density vs. Position.
3.
With the DC power off, slide the magnetic field sensor along the track until the end of the Magnetic Field Sensor in the middle of the coil and zero the sensor. Also, open the properties of the Rotary Motion Sensor and click on "Zero Sensor Now". This will make zero on the 𝑥
-axis be at the center of the coil. Also uncheck "Zero on Start".
4.
Slide the Magnetic Field Sensor back so it is about 15 cm away from the edge of the coil. Turn on Power Supply. Start recording and slowly move the Magnetic Field Sensor along the center of the track, keeping the probe parallel to the track, until the end of the sensor is about 15 cm past the other edge of the coil. Then stop recording. 5.
Explain the shape and magnitude of the plots of the parallel and perpendicular magnetic fields.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
34
E
XPERIMENT 3
—
F
ARADAY
’
S L
AW OF I
NDUCTION
Equipment
Induction Wand
EM-8099
Variable Gap Lab Magnet
EM-8641
Large Rod Base
ME-8735
45 cm Steel Rod
ME-8736
Multi Clamp
SE-9442
Wireless 3-Axis Magnetic Field Sensor
PS-3221
Wireless Rotary Motion Sensor
PS-3220
Wireless Voltage Sensor
PS-3211
Zero Gauss Chamber
EM-8652
Introduction
A voltage is induced in a coil swinging through a magnetic field. Faraday's Law and Lenz' Law are examined and the energy dissipated in a load resistor is compared to the loss of amplitude of the coil pendulum.
The maximum field between the poles of the variable gap magnet is measured directly and used to calculate the average EMF predicted by Faraday’s Law over one-half period of the pendulum. This is compared to the average induced voltage which is measured by the Voltage Sensor to verify Faraday’s Law. The strength of the magnetic field is changed by varying the magnet gap to verify the dependence on the magnetic field. The direction of the induced voltage as the coil enters and leaves the magnetic field is examined and analyzed using Lenz' Law.
In a second experiment, the Magnetic Field Sensor is mounted on the pendulum and the instantaneous EMF calculated from Faraday’s Law is graphed vs the induced voltage that is measured. The student is able to qualitatively verify Faraday’s law and analyze the factors that prevent a quantitative agreement between theory and experiment.
A resistive load is connected across the coil and the induced voltage is recorded using a Voltage Sensor, and the angle is measured with a Rotary Motion Sensor. The induced voltage is plotted versus time and angle. The power dissipated in the resistor is calculated from the voltage and the energy converted to thermal energy is determined by finding the area under the power versus time curve. This energy is compared to the loss of potential energy determined from the amplitude of the pendulum.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
35
A – Faraday's Law
Theory A
According to Faraday's Law of Induction, a changing magnetic flux, Φ
, through a coil induces an EMF given by:
? = −?
?
Φ
??
(1)
where Φ
=
∫
?
⃗ ??
= ??
and the second equality is valid if the magnetic flux density, ?
, is constant over the area, ?
, and perpendicular to the area. This is approximately true for this experiment. N is the number of turns of wire in the coil. For this experiment, the area of the coil is constant and as the coil passes into or out of the magnetic field, and Equation 1 becomes:
? = −??
?
Φ
??
(2)
Although Faraday’s Law is often written in this form, this assumes that the area is the same for each of the coils. For the coil used here, there are 200 turns and the largest has an area more than twice that of the smallest. NA is really the total area of the coils, ∑ ?
𝑖
. Doing the sum is tedious and it may be approximated (to better than 2%) as:
∑ ?
𝑖
= ?(𝜋[?
𝑎𝑣
]
2
)
(3)
where ?
𝑎𝑣
is the average radius of the coils. Equation 2 becomes:
? = −?(𝜋[?
𝑎𝑣
]
2
)
?𝐵
??
(4)
Over an interval, Δ?
, the average EMF is then give by:
?
𝑎𝑣
= −?(𝜋[?
𝑎𝑣
]
2
)
Δ𝐵
Δ?
(5)
Setup A
1.
Put a rod in the stand and clamp the cross-rod to it as shown in Fig. 3-1. Put the Rotary Motion Sensor at the end of the cross-rod.
2.
Attach the coil wand to the Rotary Motion Sensor with the tabs on the 3-step pulley just to the sides of the wand as shown in Fig. 3-2.
3.
Put the pole plates on the magnet as shown in Fig. 3-3. Adjust the gap between the magnet poles so the coil wand will be able to pass through but put the magnet poles as close together as possible (about 2.0 cm between the plates). Note that the long axis of the plates is
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
36
horizontal so the field the pendulum swings through is more uniform.
4.
Adjust the height of the coil so it is in the middle of the magnet. Align the wand from side-
to-side so it will swing through the magnet without hitting it.
5.
In PASCO Capstone, connect the Rotary Motion Sensor, Magnetic Field Sensor and Voltage Sensor. 6.
Create a Digits Display with the Perpendicular Magnetic Field Strength. Create a graph of Voltage vs. time.
7.
Plug the Voltage Sensor into the banana jacks on the end of the coil wand. Drape the Voltage Sensor wires over the rods as shown in Fig. 3-1, so the wires will not exert a torque on the coil as it swings. Fig. 3- 1: Setup.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
37
Fig. 3-2: Tabs.
Fig. 3-3: Magnet pole plates.
Procedure A
1.
Add an axis to the voltage vs. time graph and select the Perpendicular Magnetic Field Strength.
2.
Zero the Magnetic Field Sensor using the Gauss Chamber. We are only interested in the perpendicular component of the field. The position of the actual sensor is indicated by a white dot near the tip of the clear plastic rod. When the magnetic field direction is as shown in the diagram on the sensor with the field lines coming out of the side of the sensor with the label on it, the magnetic field strength will be positive. Physically, this means a magnetic north pole on the other side of the sensor and a south pole on the side of the sensor with the label.
3.
Hold the Induction Wand pendulum up out of the way. Insert the Magnetic Field Sensor probe between the magnetic pole plates as in Fig. 3-4. If the closer pole plate is a south as indicated, will the Magnetic Field Sensor be positive or negative? Click RECORD. Use the Magnetic Field Sensor to determine which pole plate is north and put a label on it. Fig. 3-4: Measuring the magnetic field strength.
4.
Use the Magnetic Field Sensor to probe the flux density between the plates. Determine the
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
38
flux density at the center of the. Also determine the distance from the edge of the plates to the point outside the plates to the left or right along the long axis of the plates where the flux density drops to 0.001 T (approximately zero field). Enter your values in the Magnetic Field Data table. Table I – Magnetic Field Data
Plate separation (cm)
Center B (T)
0.001 T distance (cm)
2
4
5.
Click STOP. Click Delete Last Run at the bottom of the screen.
6.
Let the pendulum swing freely and measure the time for 10 oscillations. Calculate the period. 7.
Pull the coil wand out a bit further than the zero field position you measured in step 4. Click RECORD and when the trace begins on the graph, release the wand and let it swing through the magnet and back. Then click STOP. Click the Scale-to-Fit Icon on the graph toolbar. The graph should show at least two up pulses and two down pulses (more is ok).
8.
Click open Data Summary at the left of the screen. Double click on Run #1 and re-label it “Strong Field”. Click Data Summary again to close the screen.
9.
Increase the magnet gap to 4.0 cm and repeat the steps 3-8, except start the pendulum from the same position you used before. Label this run as “Weak Field”. Analysis A
1.
Click the black triangle by the Run Select icon in the graph toolbar and select “Strong Field”. Click the Scale-to-Fit icon on the graph toolbar. Click the Selection icon and drag the handles on the Selection box to highlight a 1.2 s section of the data that includes the first two up pulses and first two down pulses. Click the Scale-to-Fit icon.
2.
Recall that the period of the pendulum was about 1 second. Note that there are two up peaks and two down peaks that occur in the first second of oscillation. Answer question 1 in the Conclusions A section.
3.
Click the multicolored Run Select icon and then click on the black triangle beside it and select both “Strong Field” and “Weak Field”. Answer Question 2 under Conclusions A. Use the black triangle to turn off “Weak Field”.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
39
4.
Adjust the handles on the Selection box to highlight the first pulse from where it is initially zero (or constant if it does not go exactly to zero) to where the voltage is zero between the first two pulses. Click Scale-to-Fit. Readjust the handles since you can now see the data better. Note that at the position where the voltage first begins to change, the magnetic flux density is nearly zero and at the place where the voltage crosses zero again, the magnetic flux density is maximum. Thus ΔB = B
?𝑎?
=
line 1 Center B value from the Magnetic Field Data table on the previous page. Read the
t value from the graph (time between the left and right handles on the Selection box) to the nearest 0.01 s. Greater precision is not required since the position of the left handle is pretty much a guess. Enter your values in Question 3 in the Conclusions A section.
5.
The Induction Wand specifications give the inner diameter of the coil as 1.9 cm and the outer diameter as 3.1 cm. Thus the average diameter is 2.5 cm. The specifications also give the number of turns as 200.
6.
Use the information above and Equation 5 from Theory A to calculate the average EMF. Enter your value in Question 4 under Conclusions A.
7.
Click the black triangle by the Statistics icon and select Mean. Click the Statistics icon. The mean value of the measured voltage over the highlighted interval should appear. Record it in Question 4 under Conclusions A.
Conclusions A
1.
Why are there four peaks in the first second of oscillation?
2.
Qualitatively explain the differences in the “Strong Field” and “Weak Field” curves.
3.
The values for Δ?
and Δ?
are:
4.
The values for average EMF and mean voltage are:
5.
Do your values for average EMF and measured ?
??𝑎?
support Faraday’s Law?
B – Lens’ Law Analysis
Theory B
1.
Fig. 3-5 shows a close-up of the circuit diagram printed on the Induction Wand. Note that we have connected the red plug from the Voltage Sensor to the upper port and the black plug to the lower port. If coil current flows in the direction shown by the arrows (clockwise), then the upper port becomes positive due to excess positive charge there, and the lower port becomes negative due to decrease in positive charge. Since the red lead from the Voltage
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
40
Sensor is attached to the upper port, the Voltage Sensor would read a positive voltage. Caution: Although current flow in an external circuit is from positive to negative, current flow inside a battery or power supply must be from negative to positive.
Fig. 3-5: Circuit diagram.
2.
Lens’ Law states that the current induced in a coil by a changing magnetic field through the coil will flow in a direction to oppose the change which produced it. In particular, the field produced by the induced current will be in a direction to try and prevent the field through the coil from changing.
3.
Define the positive direction for the magnetic field such that it is positive if the field lines are coming toward you if you are where the system appears as it does in Fig. 3-5. That is, if the north magnetic plate is on the side away from you (the same side as the Rotary Motion Sensor). Fill out the Lens’ Law Predictions table. The External B Field column options are: increase +, increase -, decrease +, decrease -. For example, for the first peak, since the coil is entering the field, the answer must be increase + or increase –, depending on the orientation of your magnet. The Induced Field column will be either positive or negative. The Induced Current Direction column will be either cw or ccw. The Voltage Polarity will be either pos or neg (see 1. above). Use the result from Procedure A, step 6, to answer the Table II.
Table II – Lens’ Law Predictions.
Peak #
External B field
Induced field direction
Induced current direction
Voltage Polarity
1
2
3
4
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
41
4.
For the above graph, select either run using the black triangle by the Run Select icon if necessary. Click Scale-to-Fit. Do the polarities of the voltage peaks match what you predicted in the Lens’ Law Predictions table? What does this show?
Procedure B
1.
Create the following calculations:
??? = 200 × 3.14 × [?
𝑎𝑣?
]
2
×
derivative(2,[MagneticFlux Dens(Perpendicular)],[Time])
Units of V
?
𝑎𝑣?
=0.025/2
Units of m
?
=3.3
Units of Ω
?
=4.7
Units of Ω
? = ([????𝑎𝑔?]/[? (𝛺)])
2
× ([? (𝛺)] + [? (𝛺)])
Units of W
2.
Change the graph to show Voltage and the EMF calculation on the same axis. Remove the Magnet Field axis.
3.
Use tape to mount the Magnetic Field Sensor on the Induction Wand as shown in Fig. 3-6, with the dot marking the sensor position (on the other side of the sensor probe) as near the center of the coil as possible.
Fig. 3-6: Magnetic field sensor on the induction wand.
4.
Arrange the magnet (4 cm gap) so the wand swings freely through the gap with the magnet centered on the wand when it hangs straight down.
5.
Pull the coil wand out a bit further than the zero field position you measured in step 4 of Procedure A. Click RECORD and when the trace begins on the graph, release the wand
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
42
and let it swing through the magnet and back. Then click STOP. If necessary, click the Scale-to-Fit Icon on the graph toolbar. You may need to adjust the scale on the Magnetic Flux Density by moving the hand icon over one of the numbers on the right hand scale and dragging. The graph should show at least two up pulses and two down pulses (more is ok).
6.
Note that the field between the plates is quite uniform but there is a small increase in the field strength as the sensor passes directly between the poles of the magnet. This is the reason for the stair step that showed in the voltage curve as the coil passed dead center.
7.
On the Analysis B page, Question 1, discuss the qualitative agreement between the voltage and the magnetic field shown above in terms of Faraday’s Law. Analysis B
1.
In terms of Faraday’s law, discuss the qualitative agreement of the voltage and magnetic field strength curves from graph on the Procedure B page.
2.
Highlight the EMF data by clicking on it in the Legend box. Apply maximum Smoothing to the EMF data using the slider on the graph toolbar.
3.
Click open the calculator and verify that the EMF calculated in line 1 agrees with Equation 4 (not 5) from theory A.
4.
Except near the peaks, the EMF curve calculated from the measured magnetic field using Faraday’s Law and the measured coil voltage should agree very well. The EMF peaks are too high and too narrow. In addition, the EMF peaks are too narrow at their base. All of these occur because the coil is too large compared to the dimensions of the field. Discuss how each of these deviations can be explained by the size of the coil.
5.
How well does this experiment support Faraday’s Law? C – Conservation of Energy
Theory C
If the center of mass of the pendulum starts from rest at an initial height h
i
, its potential energy is
? = ?𝑔ℎ
𝑖
.
(6)
As the pendulum swings and passes through the magnet, some energy is lost to mechanical frictional heat and some energy is converted to electrical energy and then to thermal energy in the resistance. Thus the center of mass of the pendulum does not rise to the same height but rather to a lower final height, h
2
, see Fig. 3-7. If no current is allowed to flow, the only loss is to friction and the pendulum will rise to a greater height h
3
. The energy lost to electrical heating is equal to
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
43
the difference in the final potential energy:
Electrical heat loss = ∆? = ?𝑔(ℎ
3
− ℎ
2
) = ?𝑔?[cos 𝜃
?2
− cos 𝜃
?3
]
(7)
where d is the distance from the pivot to the center of mass. This is not quite correct since there is a little less loss to friction when current flows since the pendulum does not swing as far, but the difference is small.
The thermal energy dissipated in the resistor (R) is given by
? = ∫ ??? =
Area under ?
vs. ?
graph
(8)
where ?
is the power, and ?
is time. The power is given by
? = 𝐼
2
(? + ?) = (
𝑉
?
)
2
(? + ?)
(9)
where ?
is the voltage across the resistor (
?
), 𝐼
is the current through the coil, and ?
is the resistance of the coil. See Fig. 3-8. In this experiment, ?
= 1.9 Ω and ?
= 4.7 Ω.
If energy is conserved, the energy converted to electrical heating must equal the decrease in the gravitational potential energy and thus:
? = ∆?
(10)
Fig. 3-7: Coil height decreases.
Fig.3-8: Coil and resistor circuit
Procedure C
1.
Create a Digits Display with the Angle.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
44
2.
Remove the coil wand and plug in the 4.7 Ω resistor to the end of the wand handle. Find the coil wands center of mass by balancing it on the edge of a table. Measure the distance from the pivot point to the center of mass. Determine the mass of the wand with the 4.7
resistor. Record your values in the Potential Energy Data table.
Table III – Potential Energy Data
Case
Wand mass (g)
Center of mass (cm)
Maximum angle (rad)
Wand without resistor
-----
Wand with resistor
3.
Remove the magnet pole plates. Move the magnets as close to each other as possible with enough room to just allow the coil to pass freely through. Attach the coil wand (and 4.7
resistor) to the Rotary Motion Sensor. Adjust the position of the coil so the wand is centered when hanging vertically. Plug in the Voltage Sensor as shown in Fig. 3-9. Note that the banana plugs have been turned slightly to counter the weight of the wires so the wand still hangs vertically.
4.
With the wand at rest vertically downward, click RECORD. Pull the wand sideways until the value in the Initial Angle box is as close as you can get to 0.500 rad (ignore any minus sign) and then release the wand. After the pendulum has passed its highest position on the other side, click STOP.
5.
Click open Data Summary and label this run “Loss Run”.
6.
The amount of energy lost to friction will be measured by letting the pendulum swing without the coil connected in a complete circuit. Pull the resistor plug out and plug it back in as shown in Fig. 3-10. This will disconnect the coil while not changing the center of mass or disconnecting the Voltage Sensor wires. Adjust the resistor holder angle so that the wand hangs vertically.
7.
With the wand at rest vertically downward, click RECORD. Pull the wand sideways (same direction as in step 3) until the value in the Initial Angle box is as close as you can get to 0.500 rad and then release the wand. After the pendulum has passed its highest position on the other side, click STOP. Click open Data Summary and label this run "Friction Run".
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
45
Fig. 3-9: Resistor in series.
Fig. 3-10: Resistor out of circuit.
Power Curve
1.
Create a graph of the calculation P vs. time.
2.
Click the black triangle by the Run Select icon on the graph toolbar and select Loss Run. Click Scale-to-Fit on the graph toolbar.
3.
Click open the Calculator at the left of the screen and verify that the calculation of power, P, in line 5 agrees with Equation 9 from Theory C. Click the Calculator closed.
4.
Ignore the small early peak that corresponds to you pulling the coil out of the field initially. Click on the Selection icon and drag the handles on the Selection box to highlight the second peak (the high one) which is actually two peaks corresponding to the coil moving into the field and then out of the field. Click the Scale-to-Fit icon. You should now clearly see the two peaks. If necessary, adjust the Selection box handles so no other peak is highlighted (just the two close ones). This should look like Fig. 3-11.
Fig. 3-11: Power curve.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
46
5.
Click on the Area Tool icon on the graph toolbar. The area under the curve should appear. Record the value on the Conclusion C page in the Power Curve Area table. What is the normal unit used instead of ? × ?
?
Analysis C
1.
Create a graph of Angle vs. time.
2.
Click the black triangle by the Run Select icon and select the “Loss Run”. Click the Scale-
to-Fit icon. 3.
Click on the Coordinate Tool on the graph toolbar. Verify that the angle from which you released the pendulum was close to 0.500 rad (within 0.005 rad). If not, repeat the run.
4.
Use the Coordinate Tool to measure the maximum angle that the pendulum reached on the other side. Ignore minus signs. Record this value in the Maximum Loss Angle of the Potential Energy Data table.
5.
Click the black triangle by the Run Select icon and select the “Friction Run”. Click the Scale-to-Fit icon. 6.
Use the Coordinate Tool to verify that the angle from which you released the pendulum was close to 0.500 rad (within 0.005 rad). If not, repeat the run.
7.
Use the Coordinate Tool to measure the maximum angle that the pendulum reached on the other side. Ignore minus signs. Record this value in the Maximum Friction Angle of the Potential Energy Data table.
8.
Use the data in the Potential Energy Data table and Equation 7 from Theory C to calculate the amount of gravitational energy that was lost due to the current in the coil. Enter the value in the Loss of Potential Energy table on the Conclusions C page.
Conclusions C
1.
How well does Equation 10 from Theory C check out?
2.
A serious problem here is that the resistances are so low that contact resistance becomes a real problem. You might try to check the coil resistance using a good ohmmeter. Although the coil is nominally 1.9
, there are about 3.3
between the two terminals. Click open the Calculator and replace the value for R in line 3 with 3.3 (instead of 1.9). Click open the Power Curve tab and read the new area under the curve. Record the value in the second line of the Power Curve Area table above. Now how well does Equation 10 work?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
47
E
XPERIMENT 4
—
A
MPERE
’
S L
AW
Equipment
Ampere’s Law Accessory EM-6720
Wireless 3-Axis Magnetic Field Sensor
PS-3221
Wireless Rotary Motion Sensor
PS-3220
Field Coil (500-Turn)
EM-6723
Zero Gauss Chamber
EM-8652
DC Power Supply
Ammeter
Introduction
In this experiment, we will verify Ampere’s Law experimentally by graphing the magnetic field strength that is tangent to the path taken along a closed path that encloses a current source.
The magnetic field strength is measured with a wireless magnetic field sensor which rides on a rotary motion sensor. The rotary motion sensor, which rolls on its wheel, is pushed along a closed path, Fig. 4-1.
Fig. 4-1: The coil’s magnetic field lines are shown in red. The closed path is shown as a dotted white line.
Since the magnetic field sensor element is positioned tangent to the Rotary Motion sensor’s wheel, the dot product in Ampere’s Law is performed because only the component of the magnetic field that is tangent to the path is recorded, Fig. 4-2. The current comes out of the page on the left and goes into the page on the right. The black dotted path is the closed path that encloses the left coil. The magnetic flux density is in blue.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
48
Fig. 4-2: Top view of coil (red). Theory
Ampere’s Law states:
∮ ? ⃗⃗⃗ ∙ ??
⃗⃗⃗ = 𝜇
?
?𝐼
????????
The left side of the equation can be evaluated by plotting the magnetic flux density that is tangent to the path versus the path length and then find the area under the curve. The closed integral indicates that the path traversed must be closed.
∮ ? ⃗⃗⃗ ∙ ??
⃗⃗⃗ = 𝑎??𝑎 ????? ?
∥
??. ?𝑖??𝑎??? ?????
The right side of the equation can be evaluated by determining how much current is enclosed in the path.
If you traverse a path that does not enclose any current source, the area under the curve is zero. The magnetic field of the Earth or any nearby source are measured but they will cancel out in a closed loop that encloses no current.
Setup
1.
Put the O-ring on the pulley of the Rotary Motion sensor. Attach the 3-step pulley to the Rotary Motion Sensor with the largest step closest to the Rotary Motion Sensor. Attach the Rotary Motion sensor to the sensor bracket. Do not attach the Magnetic Field sensor to the bracket yet because the sensor has to be zeroed (Fig. 4-3).
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
49
Fig. 4-3: Magnetic field sensor mounted on the rotary motion sensor.
2.
Turn on the wireless sensors. In PASCO Capstone, connect wirelessly to the Wireless Rotary Motion sensor and the Wireless 3-Axis Magnetic Field sensor. Keep the default sample rate of 20 Hz.
3.
Create a graph of the 𝑥
-axis of the Magnetic Flux Density vs. Position and a graph of the 𝑥
-axis of the Magnetic Flux Density vs. Time.
4.
Connect the DC Power Supply to the coil, with an ammeter between, and set it to voltage of 15 V (Fig. 4-4).
Fig. 4-4: Setup
5.
Create the following calculations in the Capstone calculator:
𝜇
0
?𝐼
= [Permeability constant (H/m)]
× ? × 𝐼
with units of Vs/m
?
= 500
unitless
𝐼
= Current measured with units of A
6.
Create a Digits display and select the calculation 𝜇
0
?𝐼
.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
50
Procedure A: Path Encloses Current
1.
Put a small sticker on the platform to indicate the starting position of the rotary motion sensor. Since Ampere’s Law has a closed integral, you must start and end the loop on the same point.
2.
To zero the Magnetic Field sensor, insert the probe into the Zero Gauss Chamber. You must make sure that the Magnetic Field sensor is selected in the sample rate window. Looking at the X-Magnetic Field vs. Time graph, start recording, and in the sensor’s properties, click in Zero Sensor Now. Make sure that the sensor reads zero. If not, click the zero button again.
Then stop recording and delete the last run.
3.
Attach the Magnetic Field sensor to the sensor bracket and place the wheel of the Rotary Motion sensor on your starting position. Note which direction you are pointing the Magnetic Field Sensor so you can return it to the same orientation when you return to this spot as you close the loop.
4.
Power the coil with 15 V. Measure the current through the coil. Start recording, and slowly move the sensors around the path you choose through the coil, returning to the starting point, with the sensor pointing in the same direction as when you started. Then stop recording.
5.
On the graph, find the area under the curve. Is it equal to 𝜇
0
?𝐼
? Find the percent difference.
6.
Try starting at a different spot and traversing a different closed path that encloses the coil.
7.
Try setting the voltage to 12 V so the current is different.
Procedure B: Path Does Not Enclose Current
1.
Place the wheel of the Rotary Motion sensor on your starting position.
2.
Power off the coil. Start recording. Slowly move the sensors around the path you choose through the coil, returning to the starting point. Then stop recording.
3.
On the graph, find the area under the curve. Is it equal to 𝜇
0
?𝐼
?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
51
Analysis
For the run with the current enclosed, was the area more or less than the calculated value of 𝜇
0
?𝐼
? What could account for this difference?
Compare the results from step 4, 6 and 7 in the Procedure A.
For the run with no current enclosed, select the area that is above the 𝑥
-axis to determine the positive area. Then select the area that is below the 𝑥
-axis to determine the negative area. To evaluate how close to zero the total area is, compare these areas with a percent difference.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Related Questions
The figure to the right illustrates the market for coffee in Colombia. Suppose the demand for coffee in
Colombia is DColombia and the supply in Colombia is Scolombia: The world price of coffee with free trade
is Pw
1.) Using the point drawing tool, indicate the quantity of coffee demanded at the world price (Q) in
Colombia and the quantity of coffee supplied at the world price (QS) in Colombia. Properly label each
point
2.) Using the point drawing tool, indicate the domestic market equilibrium price and quantity for coffee in
Colombia if trade were completely eliminated. Label the point 'E'
Carefully follow the instructions above, and only draw the required objects.
PW
Price per pound
Quantity (Pounds of Coffee)
SColombia
Peolombia
arrow_forward
Discussions:Voltage Distribution and String Efficiency of a Model Suspension Insulator
1- Comment on the results obtained.2- Give reasons for unequal potential distribution over the string.3- What is the effect of this un equality on the insulators?4- Can value of the string efficiency being equal to 100%. Explain your answer.5- Outline methods used to equalize the potential across the units.6- Why an insulator is represented as a capacitor C? What are the assumptionmodes?
arrow_forward
Please type out and or diagram Your solution I have bad eyesight and have a hard time reading handwriting
arrow_forward
Write the answers precisely, do not elaborate unnecessarily, and don't use chatgpt, if i caught it I'm gonna downvote Question:
Discuss the electrochemical techniques that are useful to study the capacitive properties of a material. Highlight the importance of each technique
arrow_forward
Discuss the importance of voltage regulation in power systems.
arrow_forward
List four reasons why other engineering students need to learn the fundamentals of electrical engineering.
arrow_forward
What are the primary dimensions of electric voltage (E)? (Hint: Make use of the fact that electric power is equal to voltage times current.)
When performing a dimensional analysis, one of the first steps is to list the primary dimensions of each relevant parameter. It is handy to have a table of parameters and their primary dimensions. We have started such a table for you in which we have included some of the basic parameters commonly encountered in fluid mechanics.add to this table. You should be able to build up a table with dozens of parameters
arrow_forward
In the textbox below, using your ideas of forces, partial
charges or electrons, distortions, energy, and
interactions, draw AND explain how
permanently electretized fibers in the N95 mask attract
particles of all sizes. What causes the particles to approach
the electretized fibers? (Hint: this is the essence of what your
arrow_forward
Three phase Bridge rectifier operated from a 380V, 50Hz source throughout three-phase Y/Y connected transformer with ration 2:1. The load current has continuous character with negligible ripples and average thyristor current of 15A. The circuit inductance per phase is 1.2mH. The rectified voltage due to overlapping angle is 90 % of that voltage when this angle is neglected.
1- How much will the voltage drop be due to circuit inductance *
2- How much will the dc average voltage Vdc(alpha) be.
3- How much will the firing angle be ?
4- The overlapping angle.
5- How much is the percentage change of the output dc power if the thyristors T2, T4 and T6 are replaced by three diodes D2, D4, D6.
6- How much will be the maximum RMS phase current for the mentioned in previous task circuit ( semi-converter).
7- If an additional of 1 mH inductances are added to the existing inductances in the phases , how much will the overlapping angle be. The dc load current is kept constant & the…
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,
Related Questions
- The figure to the right illustrates the market for coffee in Colombia. Suppose the demand for coffee in Colombia is DColombia and the supply in Colombia is Scolombia: The world price of coffee with free trade is Pw 1.) Using the point drawing tool, indicate the quantity of coffee demanded at the world price (Q) in Colombia and the quantity of coffee supplied at the world price (QS) in Colombia. Properly label each point 2.) Using the point drawing tool, indicate the domestic market equilibrium price and quantity for coffee in Colombia if trade were completely eliminated. Label the point 'E' Carefully follow the instructions above, and only draw the required objects. PW Price per pound Quantity (Pounds of Coffee) SColombia Peolombiaarrow_forwardDiscussions:Voltage Distribution and String Efficiency of a Model Suspension Insulator 1- Comment on the results obtained.2- Give reasons for unequal potential distribution over the string.3- What is the effect of this un equality on the insulators?4- Can value of the string efficiency being equal to 100%. Explain your answer.5- Outline methods used to equalize the potential across the units.6- Why an insulator is represented as a capacitor C? What are the assumptionmodes?arrow_forwardPlease type out and or diagram Your solution I have bad eyesight and have a hard time reading handwritingarrow_forward
- Write the answers precisely, do not elaborate unnecessarily, and don't use chatgpt, if i caught it I'm gonna downvote Question: Discuss the electrochemical techniques that are useful to study the capacitive properties of a material. Highlight the importance of each techniquearrow_forwardDiscuss the importance of voltage regulation in power systems.arrow_forwardList four reasons why other engineering students need to learn the fundamentals of electrical engineering.arrow_forward
- What are the primary dimensions of electric voltage (E)? (Hint: Make use of the fact that electric power is equal to voltage times current.) When performing a dimensional analysis, one of the first steps is to list the primary dimensions of each relevant parameter. It is handy to have a table of parameters and their primary dimensions. We have started such a table for you in which we have included some of the basic parameters commonly encountered in fluid mechanics.add to this table. You should be able to build up a table with dozens of parametersarrow_forwardIn the textbox below, using your ideas of forces, partial charges or electrons, distortions, energy, and interactions, draw AND explain how permanently electretized fibers in the N95 mask attract particles of all sizes. What causes the particles to approach the electretized fibers? (Hint: this is the essence of what yourarrow_forwardThree phase Bridge rectifier operated from a 380V, 50Hz source throughout three-phase Y/Y connected transformer with ration 2:1. The load current has continuous character with negligible ripples and average thyristor current of 15A. The circuit inductance per phase is 1.2mH. The rectified voltage due to overlapping angle is 90 % of that voltage when this angle is neglected. 1- How much will the voltage drop be due to circuit inductance * 2- How much will the dc average voltage Vdc(alpha) be. 3- How much will the firing angle be ? 4- The overlapping angle. 5- How much is the percentage change of the output dc power if the thyristors T2, T4 and T6 are replaced by three diodes D2, D4, D6. 6- How much will be the maximum RMS phase current for the mentioned in previous task circuit ( semi-converter). 7- If an additional of 1 mH inductances are added to the existing inductances in the phases , how much will the overlapping angle be. The dc load current is kept constant & the…arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,