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ELECTRIC FIELDS
OBJECTIVE: To determine the equipotential surfaces near charged objects and thus to map the electric fields
in their vicinity.
APPARATUS:
Field Mapping Board and Probe
AC Oscillator
Oscilloscope
Voltmeter
Metric Ruler
INTRODUCTION:
An electric field at a point in space is specified by the force that would act on a charge qo, when placed at that
point.
F
Equation (1)
E=
qo
In principle, one would determine the magnitude and direction of E by measuring the force F exerted on a test
charge qo. It is not feasible in general to measure the force directly, so we must use indirect means to evaluate
E.
The average electric field E, along the line between two points separated by a distance x may be calculated
from the difference in electric potential (voltage) between the points.
V2 V
Eave
Equation (2)
x
The direction of E is in the direction from higher to lower potential. Equation 2 says that the average electric
field E is equal to the space rate of change of the electric potential.
It is possible to construct an AC electric model that simulates the static electric field and potential produced by
static charges in two dimensions. One can infer the behavior of the static system from the AC model. If we can
locate points in a plane that have a constant potential, V, these points may be connected by a line, called an
equipotential line. Several lines of known potential may be drawn. Since electric fields must always be
perpendicular to these equipotential lines, we may easily construct any number of these electric field lines.
The distance between equipotential lines (and along the electric field lines) can be readily measured. Thus the
magnitude and direction of E can then be found by means of equation 2.
METHOD:
We have a conducting graphite plate with silvered electrodes to a field mapping board. An electric field, E, is
produced in the plate by connecting the plate terminals, X and Y, to a source of AC potential. The metallic
electrode at Y is connected to ground and thus has a potential of 0. The 8 series resistors divide the total
potential difference between the electrodes, X and Y, into 8 equal potential differences.
For example, if the total potential difference V = 4 Volts, then the drop of potential across each of the equal
resistances is .5 Volts. The potentials at the points 1, 2, 3, etc., relative to the reference potential at VY would
be:
A.C.
Voltmeter
V 1 = 3.5 V,
V 2 = 3 V,
V 3= 2.5 V, . . .
Oscilloscope
1
x
X
V 7 = .5 V,
VY=0V
2
3
4
5
6
Y
B
Probe
7
If we had 16 Volts (or a potential difference of 16) across the plates, we could find equipotential lines between
the plates. For instance, the series of points labeled by the potential, 6V, in figure 2 make up an equipotential
line. The horizontal lines are the electric field lines, which are always perpendicular to equipotential lines.
The points of the same potential are obtained by means of the movable probe, which is connected, to the
Cathode Ray Oscilloscope (CRO). This displays the potential difference, VAB, between the probe, and the
movable contact, which is at the position 2 on the board.
Let’s say you have the movable contact in position 2. You will move the probe to positions where the AC
signal on the oscilloscope is minimized (you’ll see a relatively flat line). When you see one you’ll put a dot on
the paper. These dots connected will form the equipotential line. All of the points along this line are then at the
same potential, V. The movable contact is then moved to position 3 and another series of points and resulting
equipotential line is obtained. In this way the entire field between the electrodes is explored and mapped.
PROCEDURE:
1.
Lift the Field Mapping board and attach the electrode configuration for two parallel plates.
2.
Fasten a sheet of paper to the upper side of the board using the tape provided.
3.
Using the appropriate template, (use the pegs on the plate) trace on the paper the electrode configuration
that is on the underside of the board. Then remove the template.
4.
Adjust the voltage output of the oscillator to 4 Volts as measured by the voltmeter.
5.
The frequency of the oscillator should be adjusted to 1000 Hz.
6.
Slide the probe onto the board so that the electrical contact on the bottom arm is below the board and the
top arm, with the hole, is above the paper.
7.
With the movable contact inserted into the board at position 1, move the probe around the board until
the oscilloscope shows a minimum signal (null). (It doesn’t have to be perfectly flat, just get close)
8.
Using a pencil, place a dot on the paper at the position of the hole in the probe arm.
9.
Move the probe to another "null" position and repeat step 8 all across the paper. The dots should be
about a centimeter or so apart so that a smooth line may be drawn.
10.
Move the contact at A to position 2 on the board and obtain the corresponding series of dots.
11.
Continue this process by moving the contact, A, through each of the positions, 1 to 7.
12.
Slide the probe off the board and remove the paper from the board. Draw a smooth line through each of
the series of dots and, at the end of the line, label these equipotential lines with their potentials.
13.
Repeat steps 1 through 13 but this time attach the electrode configuration for a point charge and a plate.
CALCULATIONS:
1.
Remembering that electric field lines must always be perpendicular to equipotential lines, draw a series
of arrowed lines ( ) to represent the electric field. Draw about 10 or 12 lines across the entire paper.
2.
Using a metric ruler, measure the distances between equipotential lines, along E-field lines, at all of the
points on the paper specified by your instructor. Measure the distance between the equipotential lines at
the place where the lines are closest together and farthest apart. Enter these 2 values for each below.
3.
Indicate on each of your field mappings where the distance measurements, X, were taken.
Using equation 2, calculate the Electric field strengths at the places specified. List the electric fields
below and box your answers. Remember to do this for each the charge configurations.
QUESTIONS:
1.
Using a voltmeter, the equipotential lines around a charged particle were found. The following lines and
their corresponding values were drawn.
Equipotential line at 3 Volts
Equipotential line at 7 Volts
Charge
a. Draw the electric field lines for this charge.
b. Using a ruler, and equation 2, calculate the average value of the electric field between the
equipotential lines.
CONCLUSION: