Experiment 14: Electric Fields andPotentials

Figure 14.1: Electric Fields and Potentials

Power Supply: Always connect the red lead to the red post and the black lead to the black post. Turn the powersupply o↵ and get a TA to check the circuit prior to plugging in the power supply.

Digital Multi-Meter (DMM) as a Voltmeter: Connect the red lead to the V/⌦ jack and the black lead to the COMjack. Turn the dial to 20V DCV and turn on. You will need to adjust the voltmeter scale (turn the dial) as youperform experiment. Adjust the scale so that you obtain the most significant figures possible without incurring anoverflow symbol (”1.”).

EQUIPMENT

Conductive/Resistive Paper (2)Electric Fields Circuit Board(2) Point Charge Connectors(2) Parallel Plate Connectors(4) Posts (2 Red, 2 Black)Tip HolderDigital Multi-Meter (DMM)Power SupplyGrease Pencil (or white colored pencil)(4) Wire Leads

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74 Experiment 14: Electric Fields and Potentials

Advance Reading

Text: Electric field, electric potential energy, equipo-tential, voltage.

Lab Manual: Appendix B - iMacAppendix C: Equipment - DMM

Objective

To map equipotential lines and electric field lines oftwo charge arrangements; to measure the electric fieldstrength of each arrangement.

Theory

Electric potential (voltage) at a point is defined asthe amount of potential energy per coulomb of chargeplaced at that point. Potential is only defined as a dif-ference in voltage between two points. This change involtage, �V , is equal to the negative of the work doneby the electric force to move a charge from one pointto another:

�V = Vb

� Va

= �W/q (14.1)

An equipotential surface is defined as a surfacewhere all points on the surface have the same electricpotential. To move a charge around on such a surfacerequires no work. In two dimensions, the equipoten-tial surfaces are equipotential lines. How close the linesare to each other is an indication of the strength of thecorresponding electric field.

An electric field, E, at a point is defined as the forceper coulomb exerted on a charge at the point:

~E = ~F/q (14.2)

Electric fields push positive charges toward a lowerstate of potential energy, or towards a lower equipoten-tial. Thus, electric field lines are always perpendicularto equipotential lines.

Electric field can also be measured by how quicklyvoltage is changing at that point, in volts/meter. Astronger electric field indicates electric potential isvarying more rapidly over a particular distance.

The two conductive patterns we investigate for thisexperiment, point charges and parallel plates, are onconductive/resistive paper.

Figure 14.2: Point Charge Arrangement

Figure 14.3: Parallel Plate Arrangement

Figure 14.4: Tip Holder

Note the 3 holes for positioning tips of wire leads.

Prelab 14: Electric Fields and Potentials 75

Name:

1. Define electric potential. State the units. (15 pts)

2. What is an equipotential surface? (20 pts)

3. Define electric field. State the units (both that are listed in the text). (20 pts)

4. Complete the statement: Electric field lines are always to equipotential surfaces.(10 pts)

5. Calculate the electric field strength of the followingarrangement. Assume the leads are 1.00 cm apartand the electric potential di↵erence measured withthe voltmeter is 0.673 V. Refer to the procedure.(20 pts)

Figure 14.5: Electric Field Strength Arrangement

76 Experiment 14: Electric Fields and Potentials

PROCEDURE

Digital Multi-Meter as Voltmeter

1. Connect a black lead to the COM jack and a redlead to the V/⌦ jack.

2. Turn the dial to 20V DCV and turn on the DMM(it is now acting as a voltmeter).

PART 1: Setup and Connections

3. Place the conductive/resistive paper on the circuitboard. Poke two holes in the paper matching theholes in the circuit board as shown in Fig. 14.2.

4. Place a point charge connector over each hole; a�xthem with one red post and one black post.

5. Connect the power supply to the point charge posts,black-to-black (ground) and red-to-red (positive).

6. Connect the voltmeter to the point charges, on topof the power supply leads.

7. Ask your TA to approve your circuit. Then, plug inthe power supply and set the voltage to 6.0 V.

8. Label the point charges with a grease pencil (theground lead is at 0.0 V, the positive lead is at 6.0 V).

PART 2: Point Charges

Equipotential Lines

9. Remove the voltmeter positive lead from the pointcharge and drag it across the conductive paper.Bring it closer to the ground lead until the volt-meter reads 1.00 V. (Adjust the voltmeter scale togive the most significant figures without getting anoverload symbol, “1.”)

10. Mark a dot at this location with the grease pencil.Move the voltmeter lead around the paper until youlocate eight points where the voltmeter reads 1.00 Vand mark each of them.

11. Connect the dots with the grease pencil to create anequipotential line. Label this line with its voltage.

12. Have your partner repeat this process to locate the2.0 V equipotential.

13. Take turns with your partner to locate the 3.0 V,4.0 V, and 5.0 V equipotentials.

Electric Field Strength

14. Measure the electric field strength (�V/�x) at the3.0 V equipotential, at the center of the paper:

(a) Measure the change in voltage between twopoints placed closely together, on either sideof the 3.0 V line. Use the clear plastic tipholder to maintain a measurable separation ofthe leads (the holes are about 1 cm apart).

(b) Calculate the field strength, in V/m, at thislocation. Record it in the table provided.

(c) Mark the location on the conductive paper andlabel the strength of the field.

Electric Field Lines

15. Place the DMM leads in each end of the tip holder.Place the positive lead immediately next to the6.0 V point charge, slightly o↵-center of a line thatwould connect the two point charges. Hold the posi-tive lead steady and pivot the ground lead around it,noticing the �V readings on the voltmeter chang-ing.

16. Pivot the black lead until you find the maximumreading on the voltmeter. Mark the location of theblack lead by pressing the tip into the paper to makean indentation.

17. Move the red lead to the indentation made by theblack lead. Pivot the black lead around this locationas before, finding the direction of greatest voltagechange.

18. Continue to “walk” the leads across the paper un-til you reach the 0.0 V point charge. Connect thedots with the grease pencil. The resulting line is anelectric field line.

19. Have your partner repeat this process, Step 15 -Step 18, beginning from a di↵erent position on the6.0 V point charge. Remove the point charge postsand conductive paper. Keep the paper as data.

PART 3: Parallel Plates

20. A�x a new sheet of conductive paper to the circuitboard using four posts as shown in Fig. 14.3. Usered posts for one parallel plate and black posts forthe other.

21. Outline the parallel plates with the grease pencil.

Experiment 14: Electric Fields and Potentials 77

Equipotentials

22. Locate the 2.0 V equipotential (as in Part 2). Con-nect the dots and label its voltage. Extend it atleast three points past the ends of the plates.

23. Have your partner repeat this process for the 4.0 Vequipotential.

Electric Field Strength

24. Measure the field strength at the center of the pa-per, between the plates (as in Part 2). Mark theposition and field strength on the paper.

25. How does this compare to the average electric fieldbetween the two plates? Calculate the average elec-tric field (�V/�x) between the plates, then find thepercent di↵erence of your measured value.

Electric Field Lines

26. It is known that the electric field between two platesis a series of parallel lines going straight from oneplate to the other. Locate and draw two of the fieldlines outside of the ends of the parallel plate con-figuration.

27. Unplug and organize the equipment on your ta-ble. Keep the conductive paper as data. Stapleone of the charge arrangements to the back of yourdatasheet; staple the other to your lab partner’sdatasheet.

QUESTIONS

1. Refer to Table 14.1. Show that the electric field unitof N/C equals V/m.

Current Amp [A] Coulomb/second

Potential Di↵erence Volt [V] Joule/Coulomb

Power Watt [W] Joule/second

Resistance Ohm [⌦] Volt/Amp

Table 14.1: Electric Quantities and Units