©98
Experiment 2
Objective: To find the equipotential surfaces in a conducting medium and to use them to plot the associated electric field.
DISCUSSION:
The electric field is the name given to that condition of space in which a charged object in the space experiences an electric force. One measure of the field is to divide the electric force on the body by the charge it carries. Since force is a vector and charge is a scalar, the field is a vector. The field is defined at each point in space and may differ both in magnitude and direction from point to point.
An equivalent method of measuring the field is to measure the potential difference between two very close points in the field and to divide this potential difference by the distance between the points. The quotient equals the component of the electric field in the direction indicated by the straight line drawn between the points. The direction of the component is toward the point at the lower potential.
If there is no potential difference between the points, that is, if the points are at the same electrical potential, the points are said to lie on an equipotential surface , which is defined to be all those points at a given potential. It can be shown that the electric field is directed perpendicularly to the surfaces of constant potential. In this lab, since we are looking at a two dimensional slice of the equipotential surface; we are observing equipotential lines , as in Fig. 1. The field points from the
Electric Field Lines region of high potential, shown by the line labeled V
1
, to the region of low potential, V
4
. The strength of the field at a given point is found by dividing the potential difference of two nearby surfaces on either side of the points by the
V1
V2
V3
V4
Figure 1: Eqipotential lines and the electric field.
perpendicular distance between them.
Equipotential Lines
2-1

In this experiment, a special conducting paper is used as the conducting medium.
Electrodes at different potentials are placed on the paper so that charge flows from one electrode to another. This flow lies along the lines of the electric field. The electrodes produce a potential difference between regions of the paper, forming lines which are at the same potential. These lines can be detected with a voltmeter; if the leads are placed in electrical contact with two different points on the conducting paper, the voltmeter indicates a potential difference only if there is a voltage drop between the points. A null, or zero, reading indicates that the leads to the voltmeter are at the same potential. The apparatus is shown in Fig. 2.
EXERCISES:
E-FIELDS BY HAND
1. Use the apparatus shown in Fig. 2 to plot curves of constant potential on the graph paper provided. Repeat this exercise for several electrodes of different shapes.
2. From the equipotential curves, construct the associated electric field. Remember that electric field lines are perpendicular to equipotential lines.
3. By finding the potential difference between two close surfaces in the neighborhood of a point, find the electric field at the point. Repeat this exercise for several
+
V
_
Figure 2: E-field mapping apparatus different points.
E-FIELDS BY CALCULATION
1.
Use the apparatus shown in Fig. 2 and the Excel template provided to plot curves of constant potential. The apparatus uses several configurations on conductive paper.
The configurations consist of two point sources, two parallel lines and a combination of one line and one point. a.
Open the EFieldLabTemplate.xls file by double-clicking on the file. (It may not work properly if you open it using the ‘Open’ command in Excel.) b.
There will be a several grids with bunches of zeros in them. This grid corresponds to the Pasco Conductive Paper. Each configuration has its own grid (scroll down to see them). c.
Using the apparatus, measure the potentials at the edge points of the paper and enter these numbers in the pink cells around the edge of the corresponding grid.
(Your computer will calculate after each point is entered). d.
Fill in the configuration potentials into the corresponding green cells (one will be zero). e.
When these steps are complete, your grid and graphs should be complete. Check the results the computer gives you against what you actually get. f.
Repeat this exercise for the other configurations.
2-2

2.
Construct and calculate the electric field. a.
Print the large equipotential plots (2D surface plots in Excel) and construct by hand the associated electric field. b.
By finding the potential difference between two close surfaces in the neighborhood of a point, find the electric field several points. c.
Repeat this exercise for each large equipotential plot.
2-3