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The Electric Field©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
Equipotential Lines
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
Electric Field Lines
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
region of high potential, shown by
V1
the line labeled V1, to the region of
V2
low potential, V4. The strength of
V3
the field at a given point is found
V4
by dividing the potential difference
of two nearby surfaces on either
Figure 1: Eqipotential lines and the electric field.
side of the points by the
perpendicular distance between them.
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
different points.
V
+
_
Figure 2: E-field mapping apparatus
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