electric field around a conducter
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electricfield.pdf
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Electric Field around a Conductor
Equipment List Qty Items Model Number
1 Voltage Sensor CI-6503
1 Equipotential and Field Mapper kit PK-9023
1 Power Supply, 15 Volts, DC SE-9720
1 Silver (nonconductive) Pen & Conductive Ink Pen PK-9031B
2 Patch cords
2 Alligator clips
Introduction The purpose of this activity is to determine the shape and magnitude of the electric field and
equipotential lines around point charge configurations and, and parallel plate configurations on a piece
of conductive paper.
Background An electric field is the effect produced by the existence of an electric charge, such as an electron
(negative charge), proton (positive charge), or ion (charged atom) in the volume of space or medium
that surrounds it. Another charge placed in the volume of space surrounding the “source” charge has a
force exerted on it. The electric force applied by two charges, q1, and q2, on each other can be obtained
from Coulomb’s Law:
𝐹𝑒 = 𝑘 |𝑞1||𝑞2|
𝑟2 , Where 𝑘 =
1
4𝜋𝜖𝑜 = 8.99𝑥109 𝑁𝑚
2
𝐶2 ⁄ , and 𝜀𝑜 = 8.85𝑥10
−12 𝐶2 𝑁𝑚2
⁄
Where k is Coulomb’s Constant, εo is the Permittivity Constant, and r is the separation distance between
the two charges.
The force of attraction or repulsion between point charges at rest act along the lines joining the two
charges. If there are more than 2 charges, the equation above hold for each pair of charges and the net
force can be found on each charge by using the superposition principle of vector addition as the vector
sum of the forces exerted on the charge by all of the other charges.
The electric field, �⃗� , at any point is defined by the electrostatic force that would be exerted on a
positive test charge qo placed there such that �⃗� = 𝐹
𝑞𝑜 =
𝑘𝑞
𝑟2 . The SI units for Electric Fields are
Volts/Meter, V/m. Electric Fields are vectors since they have both a magnitude, and a direction. Point
charges generate electric fields that point in the radial directions. Positive charges create electric fields
that radiate radially outwards, while negative charges create electric fields that radiate radially inwards.
rev 09/2016
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As mentioned earlier, electric field lines help provide a means for visualizing the magnitude and
direction of electric fields. Similarly, equipotential lines show where every point on that line has the
same potential, for example 5V, similar to that of a topographical map showing elevation, as shown
above.
It is important to note that the electric field vector at any point is tangent to a field line through that
point as you can see with the right angle indicators. Likewise, equipotential lines that are closer together
show a strong electric field and as you become further from the charges, the electric field will become
weaker shown by the distance between the field lines becoming greater.
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Setup 1. A Conductive Paper with two charge configurations will be provided. One will be two point
charges, and the other will be two parallel line charges.
2. Lay the Conductive Paper onto the Equipotential and Field Mapper kit with the side with the
charge configurations facing upwards.
3. Take two of the push-ins, and insert one into each of the points of the two point charges
configuration.
4. Open the PASCO Capstone software.
Click on Hardware Setup
If the image of the 850 PASCO Interface isn’t in the Hardware Setup window then click
on Choose Interface (if it is there skip to step 5)
Click on Automatic Detect
o In the Hardware Setup window an image of the 850 PASCO Interface should
now be there.
5. On the picture of the 850 PASCO Interface click on the Ch(A) of the Analog Inputs, then scroll
down, and select the Voltage Sensor. Now plug in the Voltage Sensor to the Ch(A) of the Analog
Inputs.
6. At the bottom of the main screen, set the sample rate of the Voltage Sensor to 10.0 Hz.
Click Signal Generator
Click on 850 Output 1.
Set the Waveform to DC, and set the DC Voltage to 5V.
Under the Voltage Limit section, set the Voltage Limit to 5V.
Set the Signal Generator to start when capture is started by clicking AUTO. (NOTE: When
changing the voltage of the signal generator, the Signal Generator must be stopped and
restarted for the change in the voltage to occur. This can be done by stopping the
capture if AUTO is selected, or by clicking OFF and then ON.)
On the right side of the main screen click and drag the Digits display into the work area.
Select Voltage (V) as the measurement.
On the Digits Display tool bar, click the icon with red arrow pointing left (should be the
second icon from the left), to reduce the displayed decimals to two.)
7. Attach the cable from the red
(positive) port of the power
supply, on the right side of the
850 PASCO Interface, to one
‘point’ charge on the conductive
paper located at 2.00 cm.
8. Attach the cable from the black
(negative) pot of the power
supply, on the right side of the
850 PASCO Interface, and the
black cable of the volt meter to
the other ‘point’ charge on the
conductive paper located at 18.00 cm.
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Procedure (Point Charge Configuration)
Part 1: Measuring the Electric Field directly between the two charges
1. Click ‘record’ to start the Voltage Sensor.
2. Starting at the positive point charge
itself use the red cable of the voltage
sensor to measure the voltage every
2.00 centimeters along the straight line
between the positive and negative point
charges. Record you’re data as Vi(V) in
Table 1 below.
The voltage reading at the
negative charge itself will be
something to the negative
fourth power. This reading is
due to ‘noise’ in the data set. Record it as ‘0.00 V’.
Part 2: Finding Equipotential lines
1. Click ‘Record’ to start the Voltage Sensor.
2. Using the red probe of the voltage sensor find a location on the conductive paper that has
voltage measurement of 1.00 V, or as close as you can get to 1.00 V.
Mark this spot with the provided silver pen.
Find at least 6 more locations on the conductive paper where the voltage is 1.00 V, or as
close as you can get, and mark each of them with the provided silver pen. Make sure the
locations you find are spread out, and not all right next to each other.
Using the provided silver pen draw a nice smooth curved line connecting all the dots
that mark a voltage value of 1.00 V. If you are capable of drawing a complete ‘circle’ on
the conductive paper with these dots do so.
Then repeat this for voltages 2.00 V, 2.50 V, 3.00 V, & 4.00V equipotential lines are.
Part 3: Finding Electric Field lines
1. Remove the black probe of the voltage sensor from the negative
point charge.
2. Hold together the ends of the voltage probes of the Voltage Sensor
so that the two tips are a fixed distance apart.
3. Set the voltage of the power supply to 5 Volts.
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4. Hold the voltage leads at an angle so the tips of the black voltage lead
touches the conductive paper at the point of an arrow and the tip of
the red voltage lead does not quite touch the paper.
5. Tilt the voltage leads upright so both tips touch the conductive paper.
Now pay attention to the voltage in the Digits Display in Capstone.
6. Keep the black tip stationary while slowly pivoting the red tip side-to-
side. When the displayed voltage is the highest, stop moving the tip of
the red voltage lead.
7. Draw an arrow on the conductive paper from the tip of the black lead
to the tip of the read lead.
8. Move the tip of the black lead to the head of the arrow you just drew.
9. Repeat steps 3 – 7 as many times needed till you have crossed the
conductive paper all the way to the other charge.
10. Then move the voltage leads back to the negative pushpin and
select a new point near the push pushpin at which to place the
tip of the black lead.
11. Repeat this whole process till you have 7 lines of arrows going
from one charge to the other charge.
12. After you have mapped the electric field, click on ‘stop’ in the
Signal Generator Tab.
Procedure (Parallel Line Charge Configuration) 1. Repeat Part 1, Part 2, and Part 3 for the configuration of two parallel line charges and enter the
data in Table 2. When measuring the voltage every 2.00 centimeters between the parallel lines start
from the middle of the positive line charge, and go straight to the middle of the negative
line charge.
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Analysis
Table 1
Two Point Charge Configuration
Vi (V) Xi (m) E (V/m)
0.020
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.180
Eavg(V/m)
1. Complete the chart by calculating the average magnitude of the electric field between each two
consecutive locations by dividing the difference in the magnitude of the voltages at each of the
two locations by the displacement between the two locations. Then find their average value and
record it in the last row. (10 points)
2. Calculate the average value of the electric field along the straight line between the two point
charges by dividing the difference in the magnitude of the voltages at the two point charges by
the displacement between the two point charges. Then take the % difference between your two
values for the average electric field between the two point charges. (5 points)
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Table 2
Two Parallel Line Charge Configuration
Vi (V) Xi (m) E (V/m)
0.020
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.180
Eavg(V/m)
3. Complete the chart by calculating the average magnitude of the electric field between each two
consecutive locations by dividing the difference in the magnitude of the voltages at each of the
two locations by the displacement between the two locations. Then find their average value and
record it in the last row. (10 points)
4. Calculate the average value of the electric field along the straight line between the two parallel
line charges by dividing the difference in the magnitude of the voltages at the two parallel lines
by the displacement between them. Then take the % difference between your two values for
the average electric field between the parallel line charges. (5 points)
5. A straight electric field line is supposed to represent a constant electric field. Does your data for
both configurations, more or less, agree with this? If not what are some plausible explanations?
(5 points)
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6. Why is your data for the parallel line configuration much more consistent than your data for the
two point charge configuration? (5 points)
7. Using one of the blank copies of the grid paper included in the hand out sketch the field lines
based on the data you obtained during this experiment for each configuration. Do your
experimental results match your expectations for these two configurations? If not, explain
possible reasons why your expectations and your experimental results are not in agreement.
(15 points)
8. What is the relationship between the density of the equipotential lines, the density of the
electric field lines and the strength of the electric field? (10 points)
9. What would happen if you placed your hand on the conductive paper while taking a
measurement? Does it affect the measurement? Why or why not? (10 points)
10. Sometimes the units for an electric field are written as N/C, while other times the units are
written as V/m, using dimensional analysis show that N/C is equal to V/m. (5 points)
