Experiment 3:

Equipotential surface and electric field lines

Objectives:

1. Learn the concepts of electric field lines and equipotential surfaces. 2. Experimentally search points, in an electric field, having the same electric potential (equipotential lines). 3. Use the equipotential lines for drawing the electric field lines.

Equipment:

A cork board, silver paint, a voltmeter, a few sheets of conducting paper, a dc power supply, and connecting wires.

Theory:

Electric field lines around a positive point charge are directed radially outward. The reason is the a when test positive charge is placed around a positive charge, they will be repelled and move radially outward. On the contrary, when test positive charges are placed around a negative charge, they will be pulled radially inward. The field lines for a single positive and a single negative point charge are as shown in the following figures.

Fig. 1: Field lines from isolated point charges

By symmetry, equipotential surfaces for the isolate charges shown above are spherical surfaces centered at the respective point charge. At any point on an equipotential surface the potential is the same and that is why they are called equipotential. In two dimensions (on paper), equipotential surfaces become equipotential lines in a similar manner that sphere become a circle. Note that a conducting surface in equilibrium is an equipotential surface. The electric filed lines on the equipotential surface must be perpendicular on the surface. This is true for any kind of complex charge distribution. Field lines and equipotential lines for isolated positive and negative point charges are shown in figures 2 and the equipotential lines and the field lines from an electric dipole are shown in figure 3.

Fig. 2

The field lines and equipotential lines around an electric dipole are shown below:

Fig. 3

The field lines and equipotential lines around a charge distribution similar to that of a parallel- plate capacitor are shown below:

In the lab, equipotential lines can be found experimentally by using a voltmeter and finding points around a certain charge distribution that are at the same voltage (electric potential). When these points are determined and marked, they may be connected to form the equipotential lines. Field lines can then be drawn perpendicular to the equipotential lines.

The types of charge distribution that will be used in this experiment are:

Fig 4 Equal and opposite point charges (an electric dipole)

Procedure:

1) Use silver pen to make electric dipole (two silver dots) types of charge distributions on the conducting paper.

2) Fix the conducting paper on the corkboard with a several sheets of regular size white paper underneath so each member of the group can have one paper.

3) Press two metallic tacks into the center of the silver spots and into the corkboard.

4) Connect the dc power supply to the tacks with appropriate wires.

5) Set the power supply to an appropriate voltage so that the voltmeter shows enough sensitivity on the conducting paper.

6) Place one terminal of the voltmeter at point A and with its other terminal search for points on the conducting paper that are equipotential with point A. At any of these points, the voltmeter should read zero. Locate a set of points that are about or at most 1 inch apart. Make a hole where each point is found by pressing a tack through the paper(s) into the corkboard.

7) Repeat steps 5 and 6 for each of points B, C, D, and E. For any of these points you will find a curved equipotential line.

8) Turn off the power, disconnect the voltmeter, and remove the tacks placed at the silver spots. Each student must obtain one sheet of white paper placed underneath the conducting paper with holes in it.

To each member of the group:

9) Circle the location of each charge and mark it as (+) or (-). The holes forming each curve must then be connected by a pencil in an artistic way such that a nice curve is obtained and not a zigzag line. This means that the line that best fits the points (holes) must be drawn, even if the line (curve) does not exactly pass through each point. (only connect the holes that are related to particular set)

10) Once all equipotential lines are drawn, the field lines can be drawn keeping in mind that anywhere a field line crosses an equipotential line the angle must be 90˚. Choose a point on one of the equipotential lines and draw a tiny line segment that is perpendicular to that equipotential line at that point. You will notice that in order for the extension of that line segment to be perpendicular to other equipotential lines, it must nicely curve to meet this property. Try to extend that tiny line segment both ways, always perpendicular to equipotential lines, until they reach the point charges. Doing this, you will be done with one field line. Draw a symmetric set of 10 field lines. The final result should be similar to Fig. 3.

Calculations:

N/A

Comparison of The Results:

Compare the experimental field lines obtained with the corresponding figures with figure 3

Conclusion: State the conclusions you can make from the experiment