Lab 1: Electric Fields and
Equipotential Lines
PHYS2120L-72, Department of Physics, University of Idaho, Moscow, 83815
Members: Nigel Clough, Aden Mead, Cooper Irwin
Introduction
The primary concept underpinning this lab is the concept of electric fields. Charged
particles exert force on other charged particles through these electric fields. Additionally these
fields are affected by other local charged particles which exert force along their own electric
fields. Fundamentally, charges with the opposite signs exert attractive forces whereas same sign
charges exert repulsive forces. Electric-field lines are a visualization of the field; they originate
on positive charge and terminate on negative charge. The direction of the field is the direction of
the force a positive test charge would experience. Notation wise, the density of the field lines
signify greater electric force.
Mathematically the Electric field can be expressed by the following formula where E is
the electric field vector, F is the electric force vector, and q is the charge.
E⃗=
F⃗
q
Furthermore, to further describe electric fields we refer to the scalar quantity: Voltage. Voltage is
a measure of electric potential which is mathematically the amount of potential energy per unit of charge.
V=
U
q
This lab deals primarily with the shape of these electric fields as well as the paths along which the
voltage describing the electric field is constant; these paths or lines are referred to as equipotential lines.
In this lab, the shape of equipotential lines will be estimated in three different setups, using voltage data
gathered with a multimeter.
Procedure
Three different setups were constructed in a water filled, styrofoam dish with positive and
negative electrodes from a DC power supply placed in the water. The first setup was just the two
electrodes as shown in figure 1.1, the second was the first setup but with a metal ring placed in
the water according to figure 1.2, and the third setup used a straight piece of metal represented in
figure 1.3. A multimeter was then used to determine the voltage at various locations in the dish
and then infer the path of equipotential lines. The electric field lines were then drawn on top,
based on the known orthogonal nature of the intersections between the electric field lines and the
equipotential lines.
Results and Analysis
The results of this experiment were recorded as sketches of the equipotential lines and
electric field lines for the three different electrode configurations, shown in Figures 1.1 through
1.3. Because this lab was primarily observational, the sketches of the measured voltage patterns
are the main data collected during the experiment.
In the first configuration, which contained only the positive and negative electrodes, the
equipotential lines were relatively symmetric and followed a predictable pattern between the two
electrodes. The electric field lines were drawn perpendicular to the equipotential lines and were
directed from the positive electrode toward the negative electrode, since electric fields point in
the direction of decreasing electric potential.
For the second and third configurations, the metal ring and metal bar changed the patterns
of the equipotential lines. The lines bent and changed shape near the added metal objects,
showing that the objects affected the electric potential in the water. Because the electric field
lines must remain perpendicular to the equipotential lines, the electric field pattern was also
distorted around the metal objects. These setups were more difficult to map because the changes
caused by the metal objects were less symmetric and harder to predict before measurements were
taken.
In all three setups, regions where the equipotential lines were closer together represented
areas of a stronger electric field. This follows from the relationship
Er = −
ΔV
Δr
because a greater change in electric potential over a smaller distance corresponds to a greater
electric field magnitude. The sketches supported the expected relationship between Voltage,
electric field lines, and equipotential lines.
Figure 1.1
Figure 1.2
Figure 1.3
Conclusion
This lab demonstrated how electric fields and equipotential lines are related. By
measuring voltage at different points in the water dish, we were able to estimate and draw
equipotential lines for each electrode arrangement. Since electric-field lines point in the direction
of decreasing electric potential, we could then draw the electric-field lines perpendicular to the
equipotential lines.
Before doing the experiment, we expected the setup with only the two electrodes to have
a mostly symmetric and predictable field pattern. The results generally matched that expectation.
The equipotential lines were more evenly shaped in the first setup, while the field was strongest
in areas where the equipotential lines were closest together. This is because a larger change in
voltage over a smaller distance corresponds to a stronger electric field.
Adding the metal ring and metal bar changed the shapes of both the equipotential lines
and the electric-field lines. We expected the metal objects to have some effect on the field, but it
was harder to predict exactly how much they would distort the pattern before taking
measurements. Our results showed that the added metal objects did noticeably alter the field and
made the equipotential lines less symmetric. Overall, the lab showed that electric-field lines are
perpendicular to equipotential lines, electric fields point from higher voltage toward lower
voltage, and a greater density of electric-field lines represents a stronger electric field.