Equipotential Surfaces
1.
Point your browser to https://phet.colorado.edu/en/simulation/charges-and-fields and
launch the simulation.
2.
Turn on the Values and Grid functions.
3.
Drag a +1 nC charge from the shielded box at the bottom of the screen and place it 0.5 m
to the left of the center of the screen. Drag a -1 nC charge from the shielded box at the
bottom of the screen and place it 0.5 m to the right of the center of the screen.
Congratulations! You have made an electric dipole!
4.
Move the voltage probe out of its box. Predict a location where it should read zero and
check your prediction. Once you have found such a location (it’s ok if you’re off by a few
thousandths), click on the pencil to mark the 0-V equipotential surface. Explain why this
shape makes sense.
5.
Find and mark equipotential contours for ± 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, and 40 V.
Observe how the electric field points—do the electric field lines always cross the surfaces
at right angles?
6.
With the aid of the measuring tape and the adjacent equipotential contours, calculate the
magnitude and direction of the electric field strength at the -5.0-V contour on the x-axis to
the right of the -1 nC charge.
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7.
Check your work using a sensor from the box. Explain any discrepancies.
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Activity 1: Capacitors in Circuits
You can make a parallel plate capacitor out of two rectangular sheets of aluminum foil
(12 cm x 12 cm) separated by pieces of paper. A textbook works well as the separator for the
foil since you can slip the two foil sheets between any number of sheets of paper and weight the
book down with something heavy and non-conducting like another massive textbook. You can
then use your digital multimeter in its capacitance mode for the measurements. Note: Insert
short wires into the capacitance slots of your multimeter as “probes”. When you measure the
capacitance of your “parallel plates,” be sure the aluminum foil pieces are arranged carefully so
they don’t touch each other and “short out.”
1. Measuring How Capacitance Depends on Area or on Separation
a. Take measurements with the foil sheets separated using increments of 50 sheets. You
will need to convert from separation in sheets to separation in meters.
separation (sheets)
50
100
150
200
250
300
350
400
450
separation (m)
capacitance (F)
b. Log into a computer and open the program Graphical Analysis. Input the separation in
meters in the X-column and the corresponding capacitance in farads in the Y-column. A
graph is automatically generated. Sketch the graph below. Is the graph linear? If the
graph is not linear, what does it look like?
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c. Now take measurements to investigate how the capacitance depends upon the area of the
foil sheets. Measure the following at 100 sheet separation. You can use the
(12 cm x 12 cm) data from the previous measurement. You will need to convert the area
to square meters.
foil sheets
4 cm x 4 cm
8 cm x 8 cm
12 cm x 12 cm
16 cm x 16 cm
20 cm x 20 cm
area (m2)
capacitance (F)
d. Log into a computer and open the program Graphical Analysis. Input the area in square
meters in the X-column and the corresponding capacitance in farads in the Y-column. A
graph is automatically generated. Sketch the graph below. Is the graph linear? If the
graph is not linear, what does it look like?
e. What is the function that best describes the relationship between spacing and
capacitance? Between area and capacitance?
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Activity 1: Capacitance and Energy
Consider the parallel plate capacitor below. At 100 V it stores 0.05 C of charge. The following
questions concern this capacitor.
100 V
0V
1.
The charge of a capacitor is directly proportional to the potential difference between the
electrodes. The constant of proportionality of called the capacitance: Q = C ΔVC . What
is the capacitance of this capacitor?
2.
What is the direction of the force a positive charge located between the plates would
experience? Recall that the potential decreases along E field lines. Sketch in the electric
field between the plates of this capacitor. Which side is positively charged, and which
side is negatively charged?
3.
Using Welec = −ΔU elec and ΔU elec = qΔV calculate how much work is done by the electric
force on one electron as it moves from the low voltage side to the high voltage side when
the capacitor is fully charged? How much work is done by the electric force on 0.05 C of
charge as it moves from the high voltage side to the low voltage side when the capacitor
is fully charged?
4.
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1
2
The electric potential energy of a capacitor is U C = Q ( ΔVC ) = C ( ΔVC ) . Why this is
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2
less than (half?) your answer above? Hint: when the capacitor is uncharged, what is the
potential difference? What is the potential difference when it if fully charged?
++++++++++++++
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H2O
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5.
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While the capacitor above is still charged, a container of water is moved between the
capacitors plates (see picture). Will the electric field in the water be greater than, less than or
equal to the electric field at the same point before the water was moved in? Why? Hint:
What caused the water to be attracted to the charged PVC Pipe?
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