Magnetic_Fields
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Smith College *
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Course
16
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
34
Uploaded by MegaSnailPerson191
Magnetic Fields
Due: 11:59pm on Monday, January 22, 2024
You will receive no credit for items you complete after the assignment is due. Grading Policy
Conceptual Question 24.1
In , suppose the magnet on the right is fixed in place and the magnet on the left is free to
pivot about its center.
Part A
Will the magnet on the left start to rotate? If so, will it initially rotate clockwise or counterclockwise?
ANSWER:
Correct
The magnet on the left will rotate in the clockwise direction because the two N poles will repel each other and the two S poles will repel
each other. Additionally the S pole of the left magnet will be attracted to the N pole of the fixed magnet and the N pole of the left magnet
to the S pole of the fixed magnet.
Conceptual Question 24.9
Part A
What is the current direction in the wire of the figure? Explain.
It will rotate in the clockwise direction.
It will rotate in the counterclockwise direction.
It will not rotate.
Typesetting math: 100%
ANSWER:
Submitted, grade pending
Conceptual Question 24.10
As shown in , a uniform magnetic field points upward, in the plane of the paper. Then the
current is turned on in a long wire perpendicular to the paper. The magnetic field at point 1
is then found to be zero.
Part A
Draw the magnetic field vector at point 2 when the current is on.
Draw the vector starting at the black dot. The location and orientation of the vector will be graded. The length of the vector will not be
graded.
ANSWER:
3751 Character(s) remaining
It is out of the page due to the right hand rule.
Typesetting math: 100%
Correct
Conceptual Question 24.11
Two concentric current loops lie in the same plane. The outer loop has twice the diameter of the inner loop. The inner loop carries a 1.5 current in a
clockwise direction.
Part A
What current should the outer loop carry such that the magnetic field in the center of the loops is zero?
Express your answer with the appropriate units.
ANSWER:
Correct
Part B
No elements selected
= 3.0 Typesetting math: 100%
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What is the direction of the current in the outer loop?
ANSWER:
Correct
Conceptual Question 24.13
The shows a solenoid as seen in cross section. Compasses are placed at points 1, 2 and 3.
Part A
In which direction will each compass point when there is a large current in the direction shown?
ANSWER:
Correct
Conceptual Question 24.16
Clockwise
Counterclockwise
The magnetic field points to the left for all three compasses in accordance with the right-hand rule for fields.
The magnetic field points to the left for compass 1 and to the right for compasses 2 and 3 in accordance with the right-hand rule for
fields.
The magnetic field points to the right for compasses 1 and 2 and to the left for compass 3 in accordance with the right-hand rule for
fields.
The magnetic field points to the right for all three compasses in accordance with the right-hand rule for fields.
The magnetic field points to the left for compasses 1 and 2 and to the right for compass 3 in accordance with the right-hand rule for
fields.
The magnetic field points to the right for compass 1 and to the left for compasses 2 and 3 in accordance with the right-hand rule for
fields.
Typesetting math: 100%
Part A
Describe the force on the charged particles after they enter the magnetic fields shown in .
ANSWER:
Correct
Part B
Describe the force on the charged particles after they enter the magnetic fields shown in .
ANSWER:
The force points toward the bottom of the page.
The force is zero.
The force points out of the page.
The force points toward the top of the page.
The force points into the page.
Typesetting math: 100%
Correct
Conceptual Question 24.18
A positive charge is moving in the direction shown in . The magnetic force on the charge is
out of the page.
Part A
Which of the magnetic field directions shown below could result in this force? There may be more than one correct answer.
Check all that apply.
ANSWER:
The force points toward the top of the page.
The force is zero.
The force points toward the bottom of the page.
The force points to the right.
The force points to the left.
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Correct
Multiple Choice Question 24.29
Two magnets with unlabeled poles are arranged as shown in . A compass points in the
direction shown.
Part A
What are the two poles 1 and 2?
ANSWER:
Correct
Multiple Choice Question 24.30
If a compass is placed above a current-carrying wire, as in the figure below, the needle will line up with the field of the wire.
1 = , 2 = 1 = , 2 = 1 = , 2 = 1 = , 2 = Typesetting math: 100%
Part A
Which of the views shows the correct orientation of the needle for the noted current direction?
ANSWER:
Correct
Multiple Choice Question 24.31
Two wires carry equal and opposite currents, as shown in the figure.
Part A
At a point directly between the two wires, the field is
ANSWER:
A
B
C
D
Typesetting math: 100%
Correct
Multiple Choice Question 24.33
A charged particle moves in a circular path in a uniform magnetic field.
Part A
Which of the following would increase the period of the particle's motion?
Check all that apply.
ANSWER:
Correct
Multiple Choice Question 24.34
Part A
If all of the particles shown in the figure are electrons, what is the direction of the magnetic field that produced the indicated deflection?
directed up, toward the top of the screen.
directed down, toward the bottom of the screen.
directed to the left.
directed to the right.
zero.
Increasing its charge
Increasing its speed
Increasing the field strength
Increasing its mass
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ANSWER:
Correct
Reading Question 24.01
Part A
A compass in a magnetic field will line up __________.
ANSWER:
Correct
Tactics Box 24.1 Right-Hand Rule for Fields
Learning Goal:
To practice Tactics Box 24.1 Right-hand rule for fields.
To find the direction of the magnetic field due to a current-carrying wire, we use the right-hand rule shown in the following Tactics Box.
TACTICS BOX 24.1 Right-hand rule for fields
Up (toward the top of the screen)
Down (toward the bottom of the screen)
Out of the plane of the screen
Into the plane of the screen
with the north pole pointing in the direction of the magnetic field
with the north pole pointing opposite the direction of the magnetic field
with the north pole pointing perpendicular to the magnetic field
Typesetting math: 100%
1. Point your right
thumb in the direction of the current.
2. Curl your fingers around the wire to indicate a circle.
3. Your fingers point in the direction of the magnetic field lines around the wire.
Part A
The following sketches show a wire carrying a current in the direction indicated. Which sketch correctly shows the magnetic field lines around
the wire?
ANSWER:
Correct
Part B
The magnetic field lines around a current-carrying wire are shown in the figure. In what direction is the current flowing in the wire?
Typesetting math: 100%
ANSWER:
Correct
Direction of the Magnetic Field due to a Wire Conceptual Question
Find the direction of the magnetic field at each of the indicated points.
For the following two questions consider the wire shown in the figure. .
Part A
What is the direction of the magnetic field at Point A?
Hint 1. The magnitude of the magnetic field due to a long, straight, current-carrying wire
The magnitude of the field is directly proportional to the current flowing in the wire and inversely proportional to the distance from
the wire:
.
Hint 2. The direction of the magnetic field due to a long, straight, current-carrying wire
The magnetic field surrounding a long, straight wire encircles the wire, as shown in the figure:
from left to right
from right to left
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The direction of the field is determined by a right-hand rule: Grasp the wire with the thumb of your right hand in the direction of the current
flow. The direction in which your fingers encircle the wire is the direction in which the magnetic field encircles the wire.
ANSWER:
Correct
Part B
What is the direction of the magnetic field at Point B?
ANSWER:
Correct
Now consider the wires shown in this figure. Note that the bottom wire carries a current of magnitude .
is out of the page.
is into the page.
is neither out of nor into the page and
.
.
is out of the page.
is into the page.
is neither out of nor into the page and
.
.
Typesetting math: 100%
Part C
What is the direction of the magnetic field at Point C?
Hint 1. How to approach the problem
To determine the direction of the magnetic field at Point C, you must determine the contribution to the field from both of the wires. The field
at Point C is the vector sum of these two contributions.
Keep in mind that if the magnetic fields are in opposite directions, the larger field will decide the direction of the net magnetic field. If they
are the same size, the net magnetic field will be zero.
Hint 2. Find the direction of the magnetic field at Point C due to wire 1
Is the magnetic field from wire 1 directed out of or into the screen at Point C?
ANSWER:
Hint 3. Find the direction of the magnetic field at Point C due to wire 2
Is the magnetic field from wire 2 directed out of or into the screen at Point C?
ANSWER:
ANSWER:
out of
into
out of
into
is out of the page.
is into the page.
is neither out of nor into the page and .
.
Typesetting math: 100%
Correct
Part D
What is the direction of the magnetic field at Point D?
Hint 1. Find the direction of the magnetic field at Point D due to wire 1
Is the magnetic field from wire 1 directed out of or into the screen at Point D?
ANSWER:
Hint 2. Find the direction of the magnetic field at Point D due to wire 2
Is the magnetic field from wire 2 directed out of or into the screen at Point D?
ANSWER:
ANSWER:
Correct
Part E
What is the direction of the magnetic field at Point E?
Hint 1. Find the direction of the magnetic field at Point E due to wire 1
Is the magnetic field from wire 1 directed out of or into the screen at Point E?
ANSWER:
out of
into
out of
into
is out of the page.
is into the page.
is neither out of nor into the page and .
.
out of
into
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Hint 2. Find the direction of the magnetic field at Point E due to wire 2
Is the magnetic field from wire 2 directed out of or into the screen at Point E?
ANSWER:
ANSWER:
Correct
Magnetic Field due to a Wire Conceptual Question
The same amount of current is flowing through two wires, labeled 1 and 2 in the figure, in the directions indicated by the arrows. In this problem you
will determine the direction of the net magnetic field at each of the indicated points (A - C).
Part A
What is the direction of the magnetic field at point A? Recall that the currents in the two wires have equal magnitudes.
Hint 1. The magnitude of the magnetic field due to a long, straight current-carrying wire
The magnitude of a magnetic field is directly proportional to the amount of current flowing in the wire and inversely proportional to
the distance from the wire:
out of
into
is out of the page.
is into the page.
is neither out of nor into the page and .
.
Typesetting math: 100%
.
Hint 2. The direction of the magnetic field due to a long, straight current-carrying wire
The magnetic field surrounding a long, straight wire encircles
the wire, as shown in the figure:
The direction
of the field is determined by a right-hand rule: Grasp the wire with the thumb of your right hand in the direction of the current
flow. The direction in which your fingers encircle the wire is the direction in which the magnetic field encircles the wire.
Hint 3. How to approach the problem
To determine the direction of the magnetic field at point A, you must determine the contribution to the field from both of the wires. The field
at point A is the vector sum of these two contributions.
Because point A is in the same plane as the wires, the contribution to the net magnetic field at point A from wire 1 or wire 2 will either point
into or out of the screen. Keep in mind that if the magnetic fields are in opposite directions, the larger field will decide the direction of the
net magnetic field. If they are the same size, the net magnetic field will be zero.
Hint 4. Find the direction of the magnetic field at point A due to wire 1
Is the magnetic field from wire 1 directed into or out of the screen at point A? Be sure to point your thumb in the direction of the current, in
this case to the right.
ANSWER:
Hint 5. Find the direction of the magnetic field at point A due to wire 2
Is the magnetic field from wire 2 directed into or out of the screen at point A? Be sure to point your thumb in the direction of the current, in
this case downward.
ANSWER:
ANSWER:
in
out
in
out
Typesetting math: 100%
Correct
Part B
What is the direction of the magnetic field at point B?
Hint 1. Find the direction of the magnetic field at point B due to wire 1
Is the magnetic field from wire 1 directed into or out of the screen at point B?
ANSWER:
Hint 2. Find the direction of the magnetic field at point B due to wire 2
Is the magnetic field from wire 2 directed into or out of the screen at point B?
ANSWER:
ANSWER:
Correct
Part C
What is the direction of the magnetic field at point C?
Hint 1. Find the direction of the magnetic field at point C due to wire 1
points out of the screen at A.
points into the screen at A.
points neither out of nor into the screen and at A.
at A.
in
out
in
out
points out of the screen at B.
points into the screen at B.
points neither out of nor into the screen and at B
at B.
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Is the magnetic field from wire 1 directed into or out of the screen at point C?
ANSWER:
Hint 2. Find the direction of the magnetic field at point C due to wire 2
Is the magnetic field from wire 2 directed into or out of the screen at point C?
ANSWER:
ANSWER:
Correct
Problem 24.1
The magnetic field 10 from a wire carrying a 1 current is 2 .
Part A
What is the field 6 from the wire?
Express your answer with the appropriate units.
ANSWER:
Correct
Problem 24.2 - Enhanced - with Video Tutor Solution
in
out
in
out
points out of the screen at C.
points into the screen at C.
points neither out of nor into the screen and at C.
at C.
= 3.3 Typesetting math: 100%
An investigator places a sample 1.0 from a wire carrying a large current; the strength of the magnetic field has a particular value at this point.
Later, she must move the sample to a 5.0 distance, but she would like to keep the field the same.
Part A
By what factor must she increase the current? ANSWER:
Correct
For the steps and strategies involved in solving this problem, you may view a Video Tutor Solution
.
Problem 24.5 - Enhanced - with Feedback
Consider the wires shown in . The upper wire carries the current = 13
.
Part A
What should the current be in the lower wire such that the magnetic field at point is zero?
Express your answer with the appropriate units.
ANSWER:
Correct
Problem 24.8
Although the evidence is weak, there has been concern in recent years over possible health effects from the magnetic fields generated by
transmission lines. A typical high-voltage transmission line is 20 off the ground and carries a current of 200 .
Part A
= 5.0
= 26 Typesetting math: 100%
Estimate the magnetic field strength on the ground underneath such a line.
Express your answer in microtesla.
ANSWER:
Correct
Part B
What percentage of the earth’s magnetic field does this represent? (Assume that magnetic field strength at the surface of the earth is
)
Express your answer in percent.
ANSWER:
Correct
Problem 24.12
The wire in carries current , which is 15 times the current of the loop; the direction of
the current in the wire is shown. The magnetic field in the center of the loop is zero. The
radius of the loop is 1.1 .
Part A
What is the direction of the current in the loop?
ANSWER:
Correct
= 2.0
= 4
Clockwise
Counterclockwise
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Part B
What is the distance from the wire to the center of the loop?
Express your answer with the appropriate units.
ANSWER:
Correct
Magnetic Force on Charged Particles Conceptual Question
For each of the situations below, a charged particle enters a region of uniform magnetic field. Determine the direction of the force on each charge due
to the magnetic field.
Part A
Determine the direction of the force on the charge due to the magnetic field.
Hint 1. Determining the direction of a magnetic force
A charged particle moving through a region of magnetic field experiences a magnetic force, unless the velocity and magnetic field are
parallel. If the velocity is parallel to the magnetic field, then the force is zero. Otherwise, the direction of the force can be found by using the
right-hand rule.
To employ the right hand rule:
1. Open your hand so that it is completely flat, and point the fingers of your right hand in the direction of the velocity vector.
2. Rotate your wrist until you can bend your fingers to point in the direction of the magnetic field.
3. The direction of your outstretched thumb is the direction of the magnetic force on a positive charge.
ANSWER:
=
5.3×10
−2
points into the page.
points out of the page.
points neither into nor out of the page and .
.
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Correct
Part B
Determine the direction of the force on the charge due to the magnetic field.
Hint 1. Determining the direction of a magnetic force
A charged particle moving through a region of magnetic field experiences a magnetic force, unless the velocity and magnetic field are
parallel. If the velocity is parallel to the magnetic field, then the force is zero. Otherwise, the direction of the force can be found by using the
right-hand rule.
To employ the right hand rule:
1. Open your hand so that it is completely flat, and point the fingers of your right hand in the direction of the velocity vector.
2. Rotate your wrist until you can bend your fingers to point in the direction of the magnetic field.
3. The direction of your outstretched thumb is the direction of the magnetic force on a positive charge.
ANSWER:
Correct
Part C
Determine the direction of the force on the charge due to the magnetic field. Note that the charge is negative.
points out of the page.
points into the page.
points neither into nor out of the page and .
.
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Hint 1. Effect of a magnetic field on a negative charge
You can use the right-hand rule to determine the direction of the force exerted on a positive charge. Once you find the direction of the force
that would be exerted on a positive charge, the force on a negative charge will point in the opposite direction.
ANSWER:
Correct
Tactics Box 24.2 Determining the Magnetic Force on a Moving Charged Particle
Learning Goal:
To practice Tactics Box 24.2 Determining the magnetic force on a moving charged particle.
When a particle of charge moves with a velocity in a magnetic field , the particle is acted upon by a force exerted by the magnetic field. To
find the direction and magnitude of this force, follow the steps in the following Tactics Box. Keep in mind that the right-hand rule for forces shown in
step 2 gives the direction of the force on a positive charge. For a negative charge, the force will be in the opposite direction.
TACTICS BOX 24.2 Determining the magnetic force on a moving charged particle
1. Note the direction of and , and find the angle between them.
2. The force is perpendicular to the plane containing and . The direction of is given by the right-hand rule.
3. For a negative charge, the force is in the direction opposite that predicted by the right hand rule.
4. The magnitude of the force is given by
or
.
points out of the page.
points into the page.
points neither into nor out of the page and .
.
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Part A
A vertical wire carries current in the upward direction. An electron is traveling parallel to the wire. What is the angle between the velocity of the
electron and the magnetic field of the wire?
Express your answer in degrees.
Hint 1. How to approach the problem
To find the direction of the magnetic field at the point where the electron is located, find the direction of the magnetic field lines at that point
using the right-hand rule for fields explained in Tactics Box 24.1. Recall that at any point the magnetic field is a vector tangent to the
magnetic field line at that point.
Hint 2. Right-hand rule for fields
1. Point your right thumb in the direction of the current.
2. Curl your fingers around the wire to indicate a circle.
3. Your fingers point in the direction of the magnetic field lines around the wire.
ANSWER:
Correct
Part B
In what direction is the force exerted by the magnetic field on the electron?
ANSWER:
= 90
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Correct
Part C
If the magnetic field of the wire is 2.5×10
−4
and the electron moves at 7.0×10
6
, what is the magnitude of the force exerted on the
electron?
Express your answer in newtons to two significant figures.
ANSWER:
Correct
Video Tutor: Magnet and Electron Beam
First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video
window and answer the question at right. You can watch the video again at any point.
Part A
The figure shows the path of a charged particle moving in a magnetic field directed into the screen.
What is the particle’s charge?
is parallel to the wire and points upward.
is parallel to the wire and points downward.
is perpendicular to the wire and points toward the wire.
is perpendicular to the wire and points away from the wire.
=
2.8×10
−16
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Hint 1. How to approach the problem.
This problem asks you to apply the concepts of circular motion and of the magnetic force on a moving charge.
Given that the particle moves in a circle, what must be the direction of the force exerted on it by the magnetic field?
Once you know that, you can use the right-hand rule to determine the charge of the particle.
ANSWER:
Correct
A negative charge gives the correct direction for the centripetal force .
Magnetic Force on a Bent Wire Conceptual Question
The bent wire circuit shown in the figure is in a region of space with a uniform magnetic field
in the +
z
direction. Current flows through the circuit in the direction indicated. Note that
segments 2 and 5 are oriented parallel to the z
axis; the other pieces are parallel to either
the x
or y axis.
Part A
Determine the direction of the magnetic force along segment 1, which carries current in the -
x
direction.
Hint 1. Magnetic force on a current-carrying wire
Electric current, by convention, is considered to be the flow of positively charged particles. Therefore, to determine the direction of the
magnetic force on a current-carrying wire, simply determine the direction of the force on a positive charge moving in the direction of the
current flow.
Hint 2. Magnetic force on segment 1
1. Point the fingers of your right hand in the direction of the current flow (to the left).
2. Rotate your hand until you can curl your fingers in the +
z
direction (directly out from the computer screen). At this point, is your palm facing the computer screen? ANSWER:
positive
negative
neutral
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ANSWER:
Correct
Part B
Determine the direction of the magnetic force along segment 2, which carries current in the -
z
direction.
Hint 1. Magnetic force on segment 2
The magnetic force is proportional to the sine of the angle between the current flow and the magnetic field. What is the angle between the
direction of current flow and the magnetic field along segment 2?
Express your answer in degrees.
ANSWER:
ANSWER:
Correct
Part C
yes
no
+
x
-
x
+
y
-
y
+
z
-
z
0
-180
+
x
-
x
+
y
-
y
+
z
-
z
0
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Determine the direction of the magnetic force along segment 3, which carries current in the +
y
direction.
Hint 1. Magnetic field on segment 3
1. Point the fingers of your right hand in the direction of the current flow (upward).
2. Rotate your hand until you can curl your fingers in the +
z
direction (directly out from the computer screen).
At this point, is your palm facing the computer screen?
ANSWER:
ANSWER:
Correct
Part D
Determine the direction of the magnetic force along segment 4, which carries current in the +
x
direction.
ANSWER:
Correct
Part E
Determine the direction of the magnetic force along segment 5, which carries current in the +
z
direction.
ANSWER:
yes
no
+
x
-
x
+
y
-
y
+
z
-
z
0
+
x
-
x
+
y
-
y
+
z
-
z
0
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Correct
Part F
Determine the direction of the magnetic force along segment 6, which carries current in the +
x
direction.
ANSWER:
Correct
Part G
Determine the direction of the magnetic force along segment 7, which carries current in the -
y
direction.
ANSWER:
Correct
+
x
-
x
+
y
-
y
+
z
-
z
0
+
x
-
x
+
y
-
y
+
z
-
z
0
+
x
-
x
+
y
-
y
+
z
-
z
0
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Problem 24.33 - Enhanced - with Video Tutor Solution
For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution
.
Part A
What magnetic field strength will levitate the 2.0 wire in the figure?
Express your answer in tesla.
ANSWER:
Correct
Part B
What is the direction of the magnetic field?
ANSWER:
Correct
Problem 24.36
A uniform 2.5 magnetic field points to the right. A 3.0-
-long wire, carrying 15 , is placed at an angle of 30
to the field, as shown in the figure.
= 0.13
Up
Down
Out of the page
Into the page
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Part A
What is the magnitude of the force on the wire?
Express your answer in newtons.
ANSWER:
Correct
Part B
What is the direction of the force on the wire?
ANSWER:
Correct
Rail Gun
A rail gun uses electromagnetic forces to accelerate a projectile to very high velocities. The basic mechanism of acceleration is relatively simple and
can be illustrated in the following example. A metal rod of mass 10.0 and electrical resistance 0.500 rests on parallel horizontal rails that have
negligible electric resistance. The rails are a distance = 10.0 apart. The rails are also connected to a voltage source providing a voltage of =
5.00 .
The rod is placed in a vertical magnetic field. The rod begins to slide when the field reaches the value = 4.90×10
−2
. Assume that the rod has a
slightly flattened bottom so that it slides instead of rolling. Use 9.80 for the magnitude of the acceleration due to gravity.
= 56
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Part A
Find , the coefficient of static friction between the rod and the rails.
Give your answer numerically.
Hint 1. How to approach the problem
The rod begins to move when the maximum force of static friction is equal to the force due to the magnetic field.
Hint 2. Find the force due to the magnetic field
What is , the magnitude of the force on the rod due to the magnetic field in this problem?
Express your answer numerically.
Hint 1. Formula for the force on the rod
The force acting on the rod is .
Hint 2. Finding the current through the rod
Find , the current in the rod. Recall that .
Express your answer numerically.
ANSWER:
ANSWER:
Hint 3. Frictional force
Recall that the maximum force of static friction is given by
, where is the magnitude of the normal force (equal to the
magnitude of the weight of the object, in this case).
ANSWER:
Correct
= 10.0
=
4.90×10
−2
= 0.5
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Score Summary:
Your score on this assignment is 96.8%.
You received 30.98 out of a possible total of 32 points.
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