electric fields lab _2

Lab 2: Electric Field and Potential of Point Charges(100 points total) You will need to run a simulation to do the lab. Answer the following questions as you work through the lab . Write your answers in blue . (Note that we may miss your response if it does not stand out ) Submit the completed lab in PDF format in Canvas before the due date. Please do not email the lab to us. An email submission will NOT be accepted. Objectives: By the end of this lab, you should be able to: 1. Map the electric field generated by a single point charge and multiple point charges. 2. Sketch electric fields accounting for their vector nature. 3. Map electric potential generated by charges as a function of distance. 4. Sketch equipotential lines. Introduction: Electric Field: A point charge (called a source charge, Q ) generates an electric field ⃗ E in the space around it. This is similar to a mass (such as Earth) generating a gravitational field near the space around it. Other charges ( q ) sense the electric field of the source charge and reacts to it. This is similar to masses reacting to the gravitational field generated by Earth. The electric field, ⃗ E , generated by a source point charge Q at a distance r is defined as the force on a positive test charge, q t (a “positive probe”) placed at that point divided by the test charge. E = F q t = k Q q t q t r 2 = k Q r 2 ; k = 9.0 × 10 9 N m 2 / C 2 is the Coulomb’s constant The direction of the electric field is the same as the direction of the force on a positive test charge . Electric Potential: The electric potential V generated by a point charge Q (source charge) at a distance r in the space around it is defined as the electric potential energy of a positive test charge q t at that location divided by the test charge q t , V = PE q t = k Q q t r q t = k Q r The unit of potential is Volts (V). Equipotential Surface: The electric potential generated by a source point charge ( Q ) will have same electric potential at certain distances from the source charge. It is possible to map these equal potential value points and form an equipotential line (or surface in 3- Dimension). Another charge, q , placed on that equipotential surface will have same electric potential energy at every point along the surface. No work is done when q is move along an equipotential surface ( a→b in the figure). Work is done in moving a charge from one equipotential surface to another equipotential surface ( a→c or b→c ). The electric potential difference ∆V between two points is the defined as the amount Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 1

of work (W) done in moving a unit positive (test) charge q between those two points. Mathematically, ∆V = V 2 − V 1 = − W q The shape of the equipotential surfaces depends upon the distribution of the source charges. Electric field lines are perpendicular to equipotential surfaces. Lab work (Remember to write your answer in a different font so that it stands out from the instructions) Part 1: Mapping Electric Field Lines Open Charges and Fields simulation https://phet.colorado.edu/en/simulations/charges-and-fields Mapping Single and Double Charge Electric Field Lines Take a few minutes to become familiar with the simulation. Click all the buttons, check what happens when you add one charge, two charges, move the charge around, change the sign of the charge. Bring in the E-field sensor, move the voltmeter. Note the numerical values when you move the charge. Once you are familiar with the simulation start the lab. 1A: Single Charge Electric Field [2+1 = 3 points] Source of charges and sensors box  Place a 1 nC positive charge and E-Field sensor (which is really a positive test charge) in the middle of the work area. Select to observe the field lines in the E-field. Move the sensor around the charge and observe the sensor’s arrow as you drag it around in the field. You can bring several sensors. You can remove a sensor by putting it back to the source box.  The sensor’s arrow illustrates the force of attraction or repulsion on a (positive) test charge by the source charge (+1nc) generating electric field. The length of the arrow is proportional to the magnitude of the force.  Replace the positive charge with a negative point charge (-1nC). To remove charges, drag them back into their source box.  The direction of the sensors arrow is ____ OUTWARD ___ or a positive charge and ___ INWARDS ___ a negative charge. (Choose from “ outwards” or “ inwards” )  As the sensor gets closer to a point charge, the field strength (length of the arrow) created by that field gets ______ STRONGER ___ (Choose from “stronger” or “weaker”). 1B: Map Single Charge Electric Field Lines  Place a positive charge at the center . Drag six sensors into the work area and place them at different locations at different distances. You should be able to map the electric field lines generated by a positive point charge. If the sensor arrows become too large, then move the sensor away from the source charge. Take a screenshot and paste your figure below . [2 points] Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 2

(a) Place two point charges at two meters (200 cm) apart as shown below. You can use the tape measure to measure the distance. Note that the unit of the tape measure (cm). The distance value does not have to be exact since it will be difficult to do so. Place more than twenty sensors around the charges to map the electric field direction. Make sure that one sensor is placed at the middle point of the two charges. Take a screenshot and paste it below. [5 points] b) Repeat the process for two negative charges. Take a screenshot and paste it below. [5 points] c) Repeat the process for one positive and one negative charge. Take a screenshot and paste it below. [5 points] Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 4

Part 2: Measuring Electric Field and Equipotential Lines On the panel in the right side, click on Voltage , Values and Grid . The tape measure is used to measure the distances from a field creating charge to a test charge. You may be able to place charges on the gridlines, without using the tape measure. It is entirely up to you. You can drag the voltmeter into the work area to measure electric potential at a location. When you bring the voltmeter to measure voltage, it includes “equipotential line” pencil. An “equipotential line” is a line, where the value of electric potential is the same everywhere along the line. When measuring the field strength at a given location, you can also draw equipotential lines by clicking on the pencil. The eraser will remove the line. 2A: Measuring electric field strength of a point charge i. Select Grid and Values. Using E-field sensor, measure the electric field strength of a 1nC positive charge: [5 points] (a) at 0.80 m ___ 12.9 ___ V/m (b) at 1.5 m ____ 3.72 ____ V/m ii. Using the E-field sensor, measure the electric field strength at 1 m (  100 cm in the tape measure) away from the 1 nC positive charge. Add another 1nC positive charge on top of the first one. What is the electric field strength now at 1m? Add two more charges (for a total of 4 nC) and measure the field strength at 1m? How is the field strength changing? (e.g., becomes half, or doubles, triples… etc.) 7.52 V/m +1nC, 15.0 V/m +2nC, 30.1 V/m +4nC becomes double. [1+1+1+2 = 5 points] E 1 ( q = 1 nC ) = ________ 7.52 V _______ Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 5

3A: Electric Feld and Electric Potential as Function of Distance from a Point Charge: Select “Values”, “Grid” . Measure the electric field and electric potential at the following distance. You may find it easier to measure these values by doing the following steps: 1. Pace a single +1nC charge at the origin (of your choice). 2. Place the tape measure on top of the charge. Make sure that the + of tape measure coincides with the center of the charge. Extend the other end of the tape to 0.2 m. The figure shows am example at 0.403 m distance from the charge . Note that the tape measure reading is in “centimeter”. We will use SI unit, “meter” for our calculations. 3. Place the field sensor on top of 0.2 m. Read the value of the electric field. It should be about 230 V/m. Place the voltmeter on top of 0.2m. (You do not need to remove the field sensor.) Read the value of the voltmeter. The reading should be near 45 Volts. Note that at this distance the voltmeter and the field sensor values are very “sensitive”. The margin of error is large. A slight variation will make a large difference in the values you read. Write the value you read. Move the voltmeter away from the charge. 4. Write those values in the table below. Repeat the steps 2 and 3 for other distances and complete the table. Table 3A: E-Field and Potential data [10 points] Distance from charge r (m) Field strength E (V/m) Potential at location V (V) 0.2 86.6 V/m 24.27 V 0.3 44.5 V/m 22.38 V 0.4 32.7 V/m 17.43 V 0.6 19.0 V/m 12.52 V 0.8 9.99 V/m 9.978 1.0 7.27 V/m 8.017 V 1.2 5.19 V/m 6.786 V 1.4 3.95 V/m 6.00 V 1.6 3.07 V/m 5.228 V 1.8 2.48 V/m 4.773 V Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 7

2.0 2.01 V/m 4.233 V 3B: Plot a graph of E vs. r and V vs. r. Paste your graph below. [10 points] You can use Excel spreadsheet to plot your graph. If you do not know how to plot in Excel, you can plot on a graph paper by hand and paste it here. Use the graph paper from the collection posted in the course Canvas page. Make two separate graphs for Evs .r and V vsr . (You may find the following video helpful if you do not know how to plot graphs in Excel. https://www.youtube.com/watch?v=Xn7Sd5Uu42A ) Insert your graphs here. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 10 20 30 40 50 60 70 80 90 100 R vs E 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 5 10 15 20 25 30 R vs V Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 8

(b) Add two more negative charges on top of the single negative charge (3 negative charges total). The extra charges should overlap the original negative charge. Repeat the process above and draw the eighteen equipotential lines. Paste the screenshot below. [5 points] (b) Add two more negative charges on top of the previous three charges (five negative charges total). Repeat the process in part (a) and draw eighteen equipotential lines. Paste the screenshot below. [3 points] Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 10

(d) Drag a sensor on the equipotential lines and move it around. Observe the angle between the electric field arrows and the equipotential lines. Approximately what angle do you see? [2 points] I would approximate it to be a 75-90 angle between the electric field arrows and equipotential lines Conclusion: Observe the nature of the equipotential lines in parts (a),(b) and (c) above. Do the equipotential lines intersect one another? Is this expected according to the theory? (Note: there is a difference between the lines intersecting and lines getting very close, but not intersecting.) [2 points] The equipotential lines do not interact one another, this is expected as according to the theory due because according the equipotential surface should travel along the single line because work is required to move to another surface. In addition to the single number theorem. Part 3: Conclusion Questions and Calculations: 1. Closer to a source point charge, the electric field strength is stronger / weaker . [1 point] Simulation created by the Physics Education Technology Project (PhET) c/o The University of Colorado at Boulder http://phet.colorado.edu/ 11