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Laboratory 2
MAPPING ELECTRIC FIELDS
Objective:
To experimentally map equipotential lines for a variety of charge configurations,
to understand their significance and their relationship to the electric field, and to see how
they compare with theoretical predictions.
Introduction:
An electric field exists around any charged body. A charge placed in this field
will experience a force tending to accelerate it in a particular direction. The direction of
the electric field at a point is the direction a positive charge would tend to move if placed
at that point.
In any electric field there are many points having the same potential. These points
are called equipotential points and a line connecting these points is called an
equipotential line. The significance of an equipotential line is that if a test charge moves
from point to point on such a line, the electric potential energy remains constant.
A line of force is the path a free test charge would follow in traversing an electric
field. The lines of force are everywhere perpendicular to equipotential lines.
It is usually easier to measure the equipotential lines in an electric field than the
lines of force. Since these lines are perpendicular to the electric field lines, it is
straightforward to subsequently determine the electric field lines. In Figure 1, the lines of
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force and the equipotential lines are depicted for two charged bodies of equal magnitude
and opposite sign.
Figure 1: Lines of Force and Equipotential Lines
In this lab we will measure a potential difference and hence establish an electric field
between two electrodes immersed in water. This will be done for a variety of electrode
configurations.
Apparatus:
-
water tray
-
graph paper
-
electrodes
-
hand held probe
-
voltmeter
-
signal generator
-
assortment of wires
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Geometries to Use:
A
B
C
Experimental Set-Up:
Signal Generator
electrode
Voltmeter
moveable
probe
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Procedure:
Perform the following steps for each of these three electrode geometries:
A. Two parallel plates.
B. Two parallel plates with a circular ring placed at the centre between them (see
Step 8 also).
C. Two circular electrodes placed about 15 cm apart.
1. Label the axes of the graph paper so that the (x, y) coordinates of points in the
tank can be read off. Place the water tray on top of the graph paper, and ensure
that the graph paper is clearly visible underneath the water tray. Add water to the
tray.
2. Connect a wire from each electrode to the signal generator. Apply a potential of
4.0 Vrms (sine wave) across the electrode with the signal generator.
3. Connect a wire from the black common “com” connection of the voltmeter to one
of the electrodes. Connect a wire from the red voltage “volts” connection of the
voltmeter to the hand held probe. The voltmeter measures the potential difference
between the probe and the electrode. Place the hand held probe on each electrode
and record the potential of each.
4. Place the hand held probe between the electrodes and move it around until the
voltmeter reads approximately 2.00 V. The voltmeter does not have to read
exactly 2.00 V, but find a point that makes the voltmeter read closer to 2.00 V
than neighbouring points within 1-2 mm. Record the (x,y)-coordinates in a table.
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Move the probe to another location where the voltmeter reads 2.00 V and record
the new (x,y)-coordinates. Continue to find points where the voltmeter reads 2.00
V and record the (x,y)-coordinates of all such locations. These points will trace
out the equipotential lines. Collect a minimum of 10 points per curve and be sure
to trace the curves as close to the edges of the tank as possible.
5. Give an error estimate of (x,y) for five or more data points along the curve. Hint:
How much movement is required to give a perceptible change in V (noting also
that the voltmeter readout has an uncertainty associated with it)?
6. Repeat step 4 for 1.0 and 3.0 volts. (Exclude the error estimates).
7. Measure the potential at several points where there are no lines, such as behind
the plates in geometry A and inside the circle in geometry B. Ensure that you have
enough points to complete the discussion. (Read the discussion requirements on
the following page!)
8. For geometry B, measure the potential at one point (the “initial point”) and then
find the point that is 1 cm from this initial point in a direction that gives the
maximum change in the voltmeter reading. E will be along the line between these
points, the magnitude of E will be E= V /d where d is the distance between the
points and the direction of E will be towards the point of lower potential.
Tabulate the x and y components of the fields along with the (x,y)-coordinates of
the field. Calculate the electric field for 4 points.
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Results and Discussion:
1. For each of the three geometries, plot the data points for each voltage on
one sheet of graph paper and use a smooth line to join the points with the
same voltage. Label the lines with the potential at that line (e.g. V = -1.0
V). Sketch the electric field lines, remembering that the electric field is at
all points perpendicular to the equipotential lines. Note: To save time, plot
the data for geometry A and geometry B on the same graph. Geometry B
will give you the same result except for the region in the center where the
circular ring is.
2. Draw a vector on the graph paper showing the direction and magnitude of
the electric field at the points used in step 8. Indicate on the bottom right
corner of the graph the scale used for plotting the electric field, i.e., the
number of N/C that a 1 cm long vector represents.
3. Calculate the electric field within the ring in geometry B. Explain this
result.
4. Draw an arrow near one electric field point that represents the direction an
electron would initially travel if placed at that point.