EC-2: Electric Fields

OBJECTIVES:

To develop an intuitive understanding of relationship between electric fields and equipotential contours and physically map electric fields in two dimensions.

APPARATUS:

Pasco power supply, (use only 0-30 V DC range); PASCO electrometer plus coaxial cables, leads & two test probes; graphitized paper on which are drawn conducting electrode configurations; field plotting board; carbon paper; pen with silver conductive ink (use cap when not in use!) shared between 4 experiments; white paper.

Figure 1: The apparatus.

Preliminary Questions:
1. Do electric fields extend through a vacuum?
2. Do electric fields extend through the interior of an insulator?
3. Do electric fields extend through the interior of a conductor?

INTRODUCTION:

To map electric fields in a plane near charged conductors we use a potential difference to produce a small current in a uniform material of high resistivity which surrounds the conductors. One locates equipotential lines between the conductors by means of probes connected to an electrometer. The lines of the electric field are perpendicular to the equipotential lines. The planar resistance material is a graphite treated piece of paper. The Pasco 0-30 V supply furnishes the current.

For the conductors we need a paint with resistance negligible compared to that of the graphitized paper. A suspension of silver flakes in a carrier which evaporates after painting, is excellent but expensive. Next best is a suspension of very fine copper or nickel flakes; we have mainly used nickel. The suspending fluid, an insulator, evaporates so slowly that recently painted electrodes are not good conductors unless special precautions and procedures are followed:

PRECAUTIONS:

1)

Use adequate ventilation. Avoid inhaling the vapor and avoid contact of the ink with your skin.

2)

Before using, shake the pen vigorously to disperse the particle matter suspended in the ink. Avoid thick layers. USE CAP THE PEN WHEN NOT IN USE.

3)

Allow 3-5 minutes for the ink to dry (at room temperature: a heat gun will speed the drying, but can easily overheat the surface causing blistering if the layer is thick).

GENERAL METHODOLOGY:

1)

Place white paper on the field plotting board, then a piece of carbon paper, and finally the graphitized paper with the conducting electrodes on the top. You may use samples already prepared or draw your own.

2)

Record the shape of the electrodes on the white paper by tracing with a hard pencil or a ball point pen.

3)

With 24 volts across the terminals of the plotting board (as in Fig. 1) check the quality of your painted electrodes by using the electrometer probe to find whether there is an appreciable potential drop along the painted electrode when you have 24 volts between the electrodes.

Figure 2: Electrode placement that qualitatively approximates a charge dipole configuration.

4)

With 24 volts connected as in Figure 1, ground the electrometer to the power supply ground. For the other electrometer lead use the sharp steel probe. Check the electrometer zero, and then move the sharp steel probe along the graphitized paper from the ground terminal A toward B until the electrometer reads +3 volts. (Hold the probe only by the insulated base, and avoid grounding the graphitized paper with your hand or you may get nonsensical results.) Press down on the sharp probe to record this location as a dot on the underlying white paper.

Map the equipotential line which corresponds to +3 volts by exploring (with the movable probe) the neighborhood of the first recorded point. Make your recorded points close enough together that you can later draw a smooth line through the points: the points need to be close together only when the direction of the equipotential changes rapidly.

NOTE: Your results, in terms of the actual voltages may vary somewhat from the idealized sketch of Fig. 1 because of contact resistance, leakage currents and other losses. To compensate you can measure the voltage at points very close to the A and B electrodes to find values $V_A$ and $V_B$ respectively and then choosing voltage steps of $(V_B-V_A)/8$.

5)

Map other equipotentials: 6 volts, 9 volts,... 21 volts.

6)

After you have drawn the equipotentials on the white sheet, dot in a few electric field lines (seven or so) as demonstrated in the right panel of Figure 1 (remembering that electric field lines are always perpendicular to equipotential contours.) latex

ALTERNATIVE METHOD: (OPTIONAL)

For one of your electrode configurations, replace the electrometer ground lead by another coaxial cable connected to a second sharp probe. Place one exploring probe about midway between electrodes A and B. Use the other probe to find positions on the paper which give zero reading on the electrometer. Since these are electric field lines as for example Fig. 1. obviously points of the same potential, they can be connected to map an equipotential line. Map three other equipotential lines approximately equally spaced on each side of the first. This method permits use of the electrometer's most sensitive voltage range and hence allows very precise location of the equipotential points. However, it does not give the potential of the equipotential line.

(NOTE: Since most existing lab electrometers are referenced to ground this only works if your DC power supply 0 V output terminal itself is not grounded.)

SUGGESTIONS:

Map equipotential lines and electric field lines for several of the configurations shown in Figs. 2 or 3 (or create your own test design). The distances are merely suggestions. Return to your instructor the graphitized paper with painted electrodes.

Figure 3: Electrode configurations for (a) parallel plates (left) and (b) ``half'' dipole (right).

Figure 4: Two other electrode configurations, (a) ligthning rod, (b) Faraday Cage.

In each case map about seven equipotential lines as continuous lines and dot in seven to nine electric field lines as dotted lines. Make clear which is which.

Turn off the electrometer when you finish mapping and place the three position switch in the grounded LOCK position.

QUESTIONS:

1. Explain in a sentence or two how you mapped the equipotential lines.
2. Pick two adjacent equipotential contours in two different electrode configurations and calculate the mean magnitude of the electric field strength where it is largest.
3. Where in Fig. 4(a) do you expect the electric field strength to be strongest? Weakest? Why do experts recommend that if you are caught outside during a thunder shower and cannot obtain shelter that you find a low spot and curl up your body? Note: there are two effects here, one from shape and the other from size, arising from the fact that lightning is caused by excessive electric fields ($> 5000\,$V/cm).

4. For Fig. 4(b) do you expect there to be appreciable electric field strength outside the confines of the box? If using the web-version of the lab manual click below on the virtual Faraday Cage demo to study this configuration in more detail.

5. Why must electric field lines be perpendicular to equipotential lines? Hint: Consider the relationship between electric potential and electric field:
   
   $$V_{b} - V_{a} = -\int_{a}^{b} \vec{E} \cdot d \vec{l}$$
   
   
   and note that V$_{b}$ = V$_{a}$ for any points $b$ and $a$ on the equipotential.)

6. For the sketch below see if you can sketch out the electric field lines. Afterwards check your answer (web-version only) by clicking below on the Like Charge Pair demo.
   

7. If you are you using the web-version of the lab manual, click on the button below to randomly place five unknown charges in a small region of space. Use any information available to determine the relative strength and sign of these five charges.