INTRODUCTION
You are probably most familiar with the concept of fields in the guise of the gravitational field. Physicists use the concept of the field to explain the interaction of particles or bodies through space, i.e., the “action-at-a-distance” force between two bodies that are not in physical contact. The earth modifies the surrounding space such that any body with mass, such as the moon, is attracted. The gravitational field gets weaker as you go farther away from the source, but never completely disappears. An electron modifies the space around it in such a way that other particles with the same charge are repelled, while particles with the opposite charge are attracted. Like the gravitational field, the electric field gets weaker with distance from the source, but is never completely gone. Any charge placed in an electric field will experience a force, as will any mass placed in a gravitational field. Just as a mass in a gravitational field has some potential energy, so does a charge in an electric field. In this lab we will examine some aspects of the electric field and the electric potential.
DISCUSSION OF PRINCIPLES
A charged body experiences a force ( F ) whenever it is placed in an electric field ( E ). The magnitude of the force, divided by the magnitude of the charge ( q ) on the body is numerically equal to the magnitude of the electric field: E = F / q . The direction of the electric field vector at any given point is the same as the direction of the force that the field exerts on a positive test charge located at that point. For example, the field due to an electron points toward the electron from all directions, since that is the direction that a positively charged body would move if placed at rest anywhere in the field.
Work, Potential Energy, and Electrostatic Potential
Work is done in moving a charged body through an electric field. The amount of work ( W ) required depends on the electric field, the magnitude of the charge and the displacement
( d ) that the charge makes through the field. When the displacement is so small that the field can be taken as uniform in the region through which the body moves, these are related by
W = F
= qE
(1)
W is the work done by the electric field. The negative of the work done by the electric force is defined as the change in electric potential energy ( U ) of the body. Put another way, it is the difference in the potential energies (Δ U ) associated with the starting and ending positions:

W
U
U final
U initial
(2)
The electrostatic potential ( V ) is defined as the electric potential energy of the body divided by its charge: V = U/q.
In terms of electrostatic potential, the work done by the electric field is
W
q
V
(3) where Δ V = V final
– V initial
, is the potential difference.
Equipotential Lines and Electric Field Lines
Specifically, let’s consider the field due to a single point charge. A point in this space near the source of the field ( i.e., near the point charge), and another point far from the source of the field are at different potentials.
This is true even if no charges reside at the two points.
All fields have points in space that are at the same potential. For example, when a point charge is the source of the field, then any two points that are the same distance from the point charge will be at the same potential. There are an infinite number of points–all lying on the same sphere–that are at the same distance, all of which are at the same potential. In three dimensions these points form a surface, called an equipotential surface.
In two dimensions–say, the equatorial plane of the sphere–the circle (equator) where the sphere intersects the plane is an equipotential line; the potential difference between any two points on this line is zero. It follows from Eq. (3) that no work is done in moving a charge along an equipotential ( i.e., an equipotential line or surface). On the other hand, it follows from Eq.
(1) that no work is done when the displacement and the field are perpendicular to one another. Therefore, the electric field vectors must be perpendicular to the equipotentials.
Because it is not simple to find the electric field lines directly, you will in this experiment first locate the equipotential lines, and then draw the field lines by knowing that they are perpendicular to the equipotential lines.
You will use the PASCO Scientific Field Mapper, which consists of a sheet of carbon-
Parallel Lines Point and Line Dipole Line and Triangle

impregnated paper. The electrodes (charged bodies) are formed by a line of conductive ink which has been drawn on the paper and then allowed to dry. You will be supplied with four electrode configurations already drawn out on conductive paper which match the copies provided here (click on the title for full-sized grid). The patterns are shown below.
1) Start with the “Parallel Lines” configuration. Connect a voltage probe (8 pin DIN connector to 2 banana plugs, figure 2.) to Analog Input A on the interface. Connect 2 banana plug cables to Output 1 on the interface. Connect the field mapper to the Pasco Universal Interface by attaching the free ends of the banana plugs to the electrodes using the metal pushpins and alligator clips. The electrodes in this part of the experiment will be acting as parallel plates. Attach the black wire from the voltage probe to the black banana plug where it connects to the
Figure 2: DIN to Banana Voltage probe electrode. The red wire from the voltage probe will be used to measure the potential at various places on the paper.
Figure 3. Capstone setup
2) Open Capstone, and click on Hardware Setup. Click on Analog Input A and choose
Voltage Sensor. Click on Signal Generator, and set the Waveform to DC for Output 1. Set the voltage to 8V, and the maximum voltage to 10V.

3) Drag a digital meter (Digits) and an analog meter (Meter) to the display area. On the bottom control bar, click “Continuous Mode” and choose “Fast Monitor Mode”. This will allow us to monitor the data without filling up the buffer with recorded data in a data run.
The red Run button will change to a red circle labeled Monitor. The setup should look like
Figure 3.
4) Begin to monitor the signal with the monitor button.. This is different from the Start button, there is no need to continuously record collected.
5) Use the free lead from the voltage probe to measure the potential at various points on the paper around the electrodes. The potential will be displayed on both of the voltmeters.
You may wish to connect the lead directly to each electrode and verify it reads what you would expect. Trace five equipotential lines until they close or leave the graph. Determine the position of the probe from the fiducial marks on the paper, and transfer the coordinates of this position to the corresponding copy.
Note : the original (black) conducting paper and the copy (white) have the same number of fiducial marks, but they are closer together on the copy than on the original, that is, the scale is different.
6) Your graph should have five equipotential lines which pass through the space between the electrodes. Construct five field lines connecting one electrode to the other. Be sure to label the voltage of each of the equipotential lines.
7) Repeat the procedure for the other configurations shown in Figure 1.
8) When you are finished, turn off the signal generator using the button in the signal generator window. Stop monitoring the data by pressing the STOP button.
9) Hand one completed diagram per team (with 5 labeled equipotential lines and 5 drawn electric field lines) to your TA with all your team member's names and the section number on the top.
Remember to close Capstone and log off the computer.
QUESTIONS FOR CONSIDERATION (You only need to explicitly answer the three questions in the lab report)
1. What are equipotential lines? How can the electric field lines be determined from them?
2. Do equipotential lines ever cross? (Think about what it would imply if they did.)
3. If it takes –68 J of work to move a –4µC test charge 2 m in an E field, what is the potential difference between the initial and final positions of the charge?

4. How can one tell from the pattern of E lines where the magnitude of E is the largest?
5. Using the triangle from this experiment as a crude model of a lightning rod, explain how a lightning rod protects buildings from lightning bolts. (Hint: Where are the electric field lines concentrated in the region around the triangle.)
6. Suppose a metal cup were placed between the electrodes in this experiment. What would happen to the electric field lines and the equipotential lines?
7. The electric-field lines are perpendicular to the equipotential lines, but how do you know that they lie in the plane of the paper?