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Page 1: ELECTRIC FIELDS AND EQUIPOTENTIALShomepage.smc.edu/morse_peter/phy22/labs/electric fields lab.pdf · ELECTRIC FIELDS AND EQUIPOTENTIALS Lab partners: ... 1) the electric field lines

ELECTRIC FIELDS AND EQUIPOTENTIALS Lab partners: 1.____________________ 2.____________________ 3.___________________

Revised: September 8, 2010

The purpose of this lab is to become comfortable drawing the “lines of force” of electric fields produced by different arrangements of electric charge. First the positions where the electric potential (or voltage) is constant will be found. These are positions where the electric potential energy for a given charge would be constant. Given these “equipotentials”, the electric field lines will be drawn.

A: GRAVITATIONAL FORCE AND FIELDS

1. Think about when we are close to the Earth’s surface. The gravitational force acting on a mass M is constant, has a magnitude of Mg, and points straight down. The diagram below shows a mass M above the Earth’s surface. For the following exercise, assume the mass M is 5.0 kg. Draw a line that passes through all the points where the gravitational potential energy of the mass would have the value of 200 joules. This means that you could place the mass anywhere along that line and it would have the same energy. Repeat this for positions where it would have gravitational potential energy of 400 J, 600 J and 800 J. (Also give an example of your work in the box below.)

The lines you drew above can be called “gravitational equipotential energy lines”.

2. Now think about what happens when we are far from the Earth and can see that the gravitational force acting on a mass is not constant as it moves. (Recall Fg = GMMearth/r

2 ) Draw on the picture below four different gravitational equipotential energy lines – you don’t have to calculate anything, just think about how the mass would have to move to not change gravitational potential energy.

Now, in a different color, draw on both diagrams the path that the mass M would follow from its position if it was allowed to move freely, but only for brief instants at a time. Continue it until it hits the Earth, and put an arrow in the middle of the line to show the direction of movement. This line is a “gravitational field line” or “line of force”. Start the mass from five other positions and draw the gravitational field lines.

The field lines give you a sense of the shape of the Earth’s gravitational field.

20m 15m 10m 5m 0m

M

Earth

M

Page 2: ELECTRIC FIELDS AND EQUIPOTENTIALShomepage.smc.edu/morse_peter/phy22/labs/electric fields lab.pdf · ELECTRIC FIELDS AND EQUIPOTENTIALS Lab partners: ... 1) the electric field lines

ELECTRIC FIELDS AND EQUIPOTENTIALS

So look back at what you’ve just found:

1) the field lines start at positions of higher gravitational potential energy and point toward positions of lower potential energy

2) the gravitational field lines are perpendicular to the equipotential lines (which also includes the surface of the Earth)

3) the direction of the field lines is the same as the direction that the mass M would move

4) the density of the field lines is directly related to the strength of the gravitational field (or gravitational force). The stronger the field, the closer the lines are to each other. (Think: if the size of the force on a mass in a region is constant, what will the spacing of the field lines look like? ____________________________________________________________ .)

B: ELECTRIC FIELD LINES AND EQUIPOTENTIALS

Electric field lines are drawn just the same way as you drew the gravitational field lines. Instead of thinking about the force that some mass M feels, now you consider what a small positive charge (a “test charge”) will feel and how it will move. Instead of gravitational equipotential lines, we have electric equipotential lines that correspond to lines of constant electric potential or voltage. These are the lines that pass through the points at which an electric charge would have constant electric potential energy. Keep in mind (in comparison to what we found when looking at gravitational field lines) that

1) the electric field lines start at positions of higher electric potential (or voltage) and point toward positions of lower electric potential

2) the electric field lines are perpendicular to the equipotential lines (which also includes the surface of the charged conductor)

3) the direction of the electric field lines is the same as the direction that a positive test charge would move

4) the density of the field lines is directly related to the strength of the electric field or electric force. The stronger the field, the closer the lines are to each other.

MATERIALS:

Equipotential plotting kit (3 sheets of conducting paper with different electrode designs, 6 push pins and 2 wires with ring connectors)

DC power supply Digital multimeter with leads 3 sheets of graph paper

3 leads (2 black, 1 red) 2 alligator clips

SETUP:

multimeter

DC power supply

probe

black lead

red lead black lead

red lead

wires with ring connectors

Page 3: ELECTRIC FIELDS AND EQUIPOTENTIALShomepage.smc.edu/morse_peter/phy22/labs/electric fields lab.pdf · ELECTRIC FIELDS AND EQUIPOTENTIALS Lab partners: ... 1) the electric field lines

ELECTRIC FIELDS AND EQUIPOTENTIALS

PROCEDURE:

1. Pin the conducting paper that has two point electrodes drawn on it to the cork board.

2. On the graph paper you are using to record data, accurately draw the positions of the electrodes.

3. Set up the equipment as shown in “SETUP”. Make sure the ring connectors on the wires make good contact with the electrodes on the conducting paper.

4. Turn on the DC power supply and allow it to warm up. Set the multimeter to read DC Volts in the range 0-20 volts. Take the probe and touch it to the pin that is connected to the ground terminal (black) of the DC power supply. The multimeter reading should be zero. If it is not, check all the connections between the wires, pushpin, and paper’s electrode.

5. Touch the probe to the other pin and adjust the power supply until the multimeter reads a voltage of 8.0 volts.

6. Hold the probe vertically and use it to find positions on the conducting paper where the voltage is 1.0 V. Record the positions where the voltage is 1.0 V on your graph paper. Record enough points so that you can easily draw a smooth curve between the points without too much guessing. Repeat the measurements for 2.0, 3.0, 4.0, 5.0, 6.0, and 7.0 V. (When using the paper with the plate and ring, don’t forget to measure points inside the ring!)

7. Repeat the measurements for the two other conducting papers: the parallel plate configuration and the plate and ring configuration.

8. When you have all the data, come show your instructor.

REPORT and ANALYSIS

Each member of the group will pick one of the pieces of graph paper and complete the following:

1. Draw smooth equipotential lines for each constant voltage recorded. Because you are drawing smooth lines, it may not be possible to pass exactly through each point you recorded – but that is fine, our experimental setup is not perfect.

2. In a different color, draw the electric field lines. Before you do this, remind yourself of what you know about field lines and how they relate to the equipotentials. Make sure you show the direction of the electric field lines.

3. Answer the appropriate question on your graph paper:

a. Two point electrodes paper: In an electrostatic situation (i.e. charges are not moving), why does it make sense for the electric field to be perpendicular to the surface of a conductor?

b. Parallel plate electrodes paper: How can you explain that the electric field lines (which also correspond to the direction a charge would feel force at that point) are perpendicular to the equipotential lines (which also correspond to places where a charge is at constant electric potential energy)? (Think about the gravitational example.)

c. Ring and plate electrodes paper: Describe fully what an equipotential is.

All three graph paper drawings and answers should be stapled to this paper and submitted.

(This lab was taken almost completely from the lab “Drawing the Lines of Force of Electric Fields Experiment” written by R. Masada.)