ECE 1813 ELECTRICITY AND MAGNETISM

Lab #1- Equipotential and Electric Field Mapping

Objectives:
- To plot the two-dimensional electric field lines between conducting parallel electrodes
- To determine the effects of conductors on the field lines.

Apparatus:
- Field mapper board,
- Digital multimeter,
- DC power supply
- semi-conductor gridded paper,
- sheets of grid paper to map the field and potential lines
- Wires.

Background Theory
In the simplest electric systems including two point charges, q1 and q2, separated by a distance r the force
that they exert on each other, FE, follows Coulomb’s Law,

𝑘𝑞1 𝑞2
𝑭𝐸 = 𝒓̂
𝑟2
Where k = 8.99×109 Nm2/C2. If the charges are electrons, then q1 = q2 = −e, where e is the elementary
charge. The force on one of the electrons is thus

𝑘𝑒 2
𝑭𝐸 = 𝒓̂
𝑟2
Charges with the same sign repel and charges with opposite signs attract, so these electrons will repel each
other. If we want to hold these two electrons at that constant distance r, we must balance the repelling forces
by exerting an equal force inward, much like compressing a spring to prevent from expansion.

Electric potential

To hold the electrons at distance r from each other we must do work and expend some energy. This energy is
“stored” as potential energy in the 2-electronsystem. Thus, the force between objects is related to the
potential energy of the system. Notice that to reduce the distant between the electrons to a half of the original
distance, the force must be 4 times greater than the original force.

The work done by a constant force F that causes a displacement of x equals

W = F Δx
1
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ECE1813 - Lab #1- Equipotential and Electric Field Mapping

The required force to maintain the system of the two-electron, however, is not a constant force but changes
with distance. Applying some elaborate math to the Coulomb’s law we will find the stored energy (or the so-
called potential energy, U) between q1 and q2 to be

𝑘𝑞1 𝑞2
𝑈=
𝑟

Note: The electric potential energy is not the same as “electric potential”. But, then, what is the electric
potential?

The electric potential is a quantity concerning the electric quality of space around one charge regardless of
the presence of the other charge. In other words, the electric potential V , is defined to be the electric
potential energy divided by q2, the charge that is feeling the force:

𝑈 𝑘𝑞1
𝑉= =
𝑞2 𝑟

Then the above formula provides the electric potential due to q1. Note that the electric potential is also
sometimes called voltage. If you make a map of electric potential values at different points, you can then
draw equipotential lines that connect all the points that have the same potential (or voltage).

Relationship between the Electric field lines and Equipotential lines

The electric field is the agent that exerts an electric force on a charged particle. The electric field is defined
as the force exerted on a test/probe charge (e.g. q2) placed at a distance r from a source charge. When the
source is a point charge the electric field is

𝑭𝐸 𝑘𝑞1
𝑬= = 2 𝒓̂
𝑞2 𝑟

Moving a charged particle in a space filled with an electric field requires work, unless the particle is
displaced along an equipotential line (2D) or equipotential surface (3D). To better understand the concept,
visualize the potential field as a hill. The higher the elevation the greater the potential. If we place a ball on
the top of the hill it will roll downward, from a higher to a lower potential (remember the gravitational
potential energy is mgh, where h is the height). If you place the ball on a path whose elevation is same
around the hill, the ball will not move at all, since that path is an equipotential path. In this case the change
in gravitation potential over a displacement is related to the gravitational field (g). Likewise the change in
electric potential over a certain displacement is called the electric field, and is formulized as

|∆𝑉|
|𝐸| =
∆𝑥

where ΔV is the change in the potential (or voltage) and Δx is the distance. The relationship between the
electric field lines and equipotential lines can be summarized as
2

- They are perpendicular to each other.

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- The electric field lines point in the direction of decreasing potential.

ECE1813 - Lab #1- Equipotential and Electric Field Mapping

Procedure
a. Connect the apparatus as shown in Figure 1. The first template will consist of two parallel conducting
electrodes. This can be thought of a 2D model of parallel plate capacitor. One electrode will be
connected to the positive terminal of the power supply and the other electrode to the negative terminal
which will be your reference. Make sure the multimeter is connected as shown.

POWER SUPPLY

VOLTMETER

Figure 1. Equipotential Lines

b. Adjust the power supply so that it is supplying 12.2 volts. Make sure that the electrode to which the
negative side of the power supply is connected is 0.0 volts at each of its ends. Also make sure that the
other electrode is 12 volts or more at its ends.

Your hand will conduct as well as the semiconductor carbon paper; make sure you keep it off the paper
while making measurements. A firm and steady pressure on the probe will be required. However, care
should be taken not to poke holes in the paper by pressing too hard.

c. On a grid sheet paper prepare a scale map of each electrode arrangement. Locate a point where the
voltage reads 1 volt and plot it on your map. Plot a sufficient number of similar points to show the shape
of the 1 volt “contour curve”. Repeat the process for 3,5,6,8 and 10 volt “contours”.
d. Measure the distance delectrodes between the parallel plates and assign a reasonable uncertainty to this
measurement. Use this measured distance and the 12.2 V electric potential difference between the plates
to calculate the electric field between the plates and its uncertainty.
e. Measure the distance xlines between two of your lines of equipotential; calculate the difference in
electric potential between these two lines; calculate the electric field.
f. Draw and label at least eight electric field lines. You should include at least 2 field lines near the edges
of the electrodes
g. Indicate the direction of the electric field with an arrow on each of your electric field lines.
h. Except steps d. and e. repeat the procedure with the circular conductor between the electrodes.
Using your results, you may want to address the following subjects in your conclusion
- where the electric field lines curve the most with comments.
- the potential of the circular conductor with comments.
- the potential inside the circular conductor with comments
3

- the way the circular conductor distorted the electric field lines with comments.
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ECE1813 - Lab #1- Equipotential and Electric Field Mapping