Experiment 6
Mapping the Electric Field
Preparation
Prepare for this week's quiz by reading the material in your textbook covering electric fields,
field lines, work done on a charge, electric potential, and equipotential lines. Prepare your graph
paper for the experiment. (In other words, follow the directions at the start of the procedure
section.)
Principles
An electric field, E, exists anywhere a stationary test charge, qo, experiences an electric force, F.
E and F are vector quantities and the relationship between them is given by
E =
F
.
qo
qo is assumed to be positive and very small. E and F are always in the same direction.
Electric field lines are imaginary lines used to visualize electric fields. The lines always leave
positive charges and enter negative charges. They are closer together where the field is stronger
and they never cross. The lines indicated the direction of the force acting on a test charge placed
at that point.
If a positive test charge is released in an electric field it will move away from the positive side of
the field toward the negative side. The field will do work on the charge as is moves from point
A to point B according to
B
B
A
A
W=⌠
⌡F . ds = ⌠
⌡F ds cos θ .
Since the electric force is a conservative force, there will also be a change in potential energy,
∆U = -W .
The change in potential energy per unit charge is a scalar quantity called the electric potential, V.
Electric potential is always measured between two points.
In any field there exists a set of points between which there is no potential difference. A set of
such points will make up an equipotential surface. This surface is always perpendicular to the
electric field. In other words, when F and ds are perpendicular, θ equals π/2 and cosθ equals
zero. No work is done moving a charge along such a surface.
Electric potential, or voltage, is easily measured. This phenomenon can be used to map an
electric field.
In this experiment you will investigate the electric field around a pair of cylindrical electrodes
and around a pair of flat plates. To this you will find equipotential lines using a voltmeter. The
meter works by registering very small currents that flow as a result of the potential difference.
The air between the charged electrodes in this experiment will not conduct enough current for
the voltmeter to work. Therefore you will fill the apparatus with water. Pure water is actually an
insulator, but the chlorine in tap water will allow it to conduct a small current.
Figure 1. The field around two
cylindrical electrodes.
Figure 2. The field around two flat electrodes.
The electrodes attach to a piece of Plexiglas which is marked with a grid. You will measure the
potential difference between many different points and the negative electrode and map points
where the potential has certain values onto graph paper.
Figure 3. The water tray.
Equipment
1
2
2
1
2
3
1
1
tray with Plexiglas grid
cylindrical electrodes
flat electrodes
multimeter
alligator clips
black banana wires
red probe lead
floating LED
Procedure
Usually electricity and water are not a good combination. This experiment is, however, perfectly
safe. Make sure your instructor checks your wiring before you make the final connection
to the power supply.
1.
You will need two sheets of 10 lines per centimeter Cartesian graph paper. The scale for
the graphs is 1 cm = 1 cm, do not even think about using any other scale. Draw a set of
coordinate axes on each piece of paper so that the origin is in the center. Make the lines
heavy. Label the long axis x and the short axis y for each. On one sheet draw two heavy
circles 1.3 cm in diameter centered at the points (7.6, 0.0) and (-7.6, 0.0). If you don't have
a compass, wait until you get to the lab; you can use one of the actual electrodes as a
template to draw the circles.
2.
On the other sheet draw one heavy line between the points (-7.6, 7.6) and (7.6, 7.6) and
another line between the points (-7.6, -7.6) and (7.6, -7.6)
3.
Place the mounted transparent graph paper in the tray and put in one of the two sets of
electrodes. Add water until the entire electrode is covered with water. Attach a red wire to
one electrode and a black wire to the other. Have your instructor check your wiring and
then connect the other electrode to the positive power supply output. Do not touch the
terminals with your bare skin. If you touch both terminals at the same time you will be
mildly shocked.
4.
Set the function switch of the multimeter to DCV. Connect the negative lead to the wire
that leads to the negative electrode where it is attached to the wall. This is the same as
connecting the wire to the negative electrode itself, but it keeps you from having too many
wires stacked up in the water tray.
5.
The multimeter has a little stand attached to its back. You can use this to position the meter
so you can read it without having to pick it up each time. The voltage input is labeled, if
you are uncertain ask your instructor which input to use. Plug the red probe wire into the
correct input. Push the "Range" switch until your display shows one decimal place. Do
not attempt to take readings to greater accuracy, you will waste time and drive yourself
crazy.
6.
Place the positive probe in the water and move it away from the negative terminal along the
x-axis until the meter reads 10 Volts. Record this position on your graph paper. Be sure
that you keep the positive probe vertical in the water and that you do not push down hard
on the probe. It is easiest to try to keep the probe moving along one of the heavy lines, this
makes it easier to read the points.
7.
Move the probe around in the water to find a number of points where the meter reads 10
Volts. Look at points all around the electrodes, all over the grid. The points should be one
to two cm apart. They should be closer together where the lines are changing direction,
farther apart where the field is more uniform.
8.
Plot the points directly onto the graph paper. Do not write down the coordinates.
9.
Unplug the wires from the power supply and change to the other set of electrodes. Repeat
the procedure.
10.
Sketch in your equipotential lines. Predict where the field lines will go. Place the LED
‘float’ on the surface of the water and push it around with your pen or pencil. It will light
up when the arrow points in the same direction as the electric field. Do your predictions
agree with what you see?
11.
How brave are you? When you have finished place one finger of each hand in the water at
about the 10 Volt line. Hold one finger still and slowly move the other toward the positive
electrode until you begin to feel the effect of the electric field. Record the potential
difference between your two fingers. No, you will not electrocute yourself.
12.
Turn off the meter, disconnect the wires, remove the electrodes and empty the water from
the tray. Put the equipment back where you found it.
Data
Data should consist of the points along the equipotential surfaces for the two sets of electrodes.
Indicate the voltage at each surface.
Analysis
1.
Draw the best fitting dashed line that describes the first set of points and label it 10 V. This
is an equipotential line. This should be a smooth line that best represents the data, do not
merely connect the dots. Repeat this for the 20, 30, and 40 V equipotential lines.
2.
Draw in solid lines to represent the electric field between the two electrodes for each set of
measurements. Remember the rules for field lines. Use arrows to indicate the direction of
the field. Show as much of the field as possible.
3.
The electric field between the copper strips is fairly uniform. Use the distance between the
centers of the electrodes and the definition of potential difference to calculate its
magnitude.
Questions
Answer these questions in as much detail as you can.
1.
Define potential difference. What is the difference between electric potential and electric
potential energy? What is the unit for potential difference?
2.
What two units are used for electric fields? Write out the units of both to show that they
are equivalent.
3.
Why are the electric field lines always perpendicular to equipotential lines?
4.
Why can electric field lines never cross?
5.
The LED will only light up if enough electrical current is flowing through it. The amount
of current is given by I = V/R, where V is the potential difference. Why does it only light
up when it is pointing in the same direction as the electric field?
If it applies to you, write "I have not cheated on this lab report" and sign your name.
Grading
4 pts
3 pts
Data and Analysis.
For each question.