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PHY 134 Lab 1 ­ Electric Field Plotting [Stony Brook Physics Laboratory Manuals]
Stony Brook Physics Laboratory Manuals
PHY 134 Lab 1 - Electric Field Plotting
The purpose of this lab is to develop the concept of electric field (E )⃗ and electric potential (V ) by investigating the space between
a pair of electrodes connected to a source of direct current (DC) electricity. You will plot equipotential lines (lines of equal electric
potential) and sketch in lines representing the electric field between the electrodes.
Equipment
1 digital voltmeter
2 voltage probes (one right-angle “fixed” one and one right-angle “handheld” one)
insulated wire leads (2 red ones and 2 black ones) with banana plugs at each end
1 platform (with springy metal clips to hold down acetate sheets and make electrical contact to opposing silver-paint regions)
2 carbonized acetate sheets (one with a “parallel plate” configuration, and one with an “electric dipole” configuration) to be
mounted under the springy metal clips on the platform
1 power source or battery (approximately 3.0V variable power supply or approximately 1.5V DC fixed battery)
1 meter stick
handed out in lab: 2 photocopied grid-point sheets (with “parallel plate” and “electric dipole” configurations)
Introduction
Every electrically charged object produces an electric field around it at all points in space – similar to the way an object with mass
produces a gravitational field around it at all points in space – affecting all other surrounding charged objects. The properties of this
field are entirely determined by this “source” charge. In the case of a positive point charge, as shown in the image below, the electric
field (E )⃗ points radially outward in all directions. The magnitude (or “strength”) of this field is greatest where the density of electric
field lines is highest; in the image, the lines are most dense near the point charge, where ∣∣E ∣∣⃗ is greatest, and the lines are least dense
radially away from the point charge, where ∣∣E ∣∣⃗ is least. Thus, we can express the electric field produced by a single point charge as:
⃗ E =
where ε0
= 8.85 × 10
−12
C
2
N⋅m
2
1
Q
4πε0
r
^
r
(1)
is the permittivity of free space, Q is the electric charge of the source point charge, r is the
radius/distance away from the point charge at which the electric field is being considered, and r^ is the unit vector pointing radially
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(
→ −
)
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away from the point charge. Note that, if the source was negatively charged (Q → −Q), the direction of the electric field would
be −r^, towards the point charge. Therefore, electric field lines radiate away from positive charges and terminate at negative charges.
Because the electric field has both a magnitude and a direction, it is known as a vector field.
This electric field surrounding charged objects is therefore analogous to the gravitational field surrounding all massive objects. Given
the properties of a nearby test charge q at a radius/distance r , one can determine the electric force acting on the test charge:
∣ F ∣⃗ =
∣
∣
1
4πε0
Qq
r
(2)
2
where the direction of the force is either away from the source charge (if both charges have the same sign), or towards it (if the
charges have opposite signs). Hence, a positive test charge placed in the electric field of a positive source charge moves radially away,
in the direction of the electric field, whereas a negative test charge moves radially towards the positive source charge, in the opposite
direction of the electric field.
This “rule” of opposite charges attracting and like charges repelling each other, however, does not have an intuitive explanation
based on these definitions. To understand this phenomenon, we introduce the quantity called electric potential (V ) , measured in Volts
(not to be confused with electric potential energy, which is measured in Joules!). The electric potential measures the ability (or
“potential”) for a source charge to interact with a nearby test charge. In a sense, positive charges are sources of positive electric
potential, while negative charges are sources of negative electric potential. For a point source, the electric potential is given by:
1
Q
4πε0
r
V =
(3)
The electric potential has magnitude but no direction; it is a scalar field. To represent this field graphically, lines of equal electric
potential, called equipotential lines, are drawn around the source charge. As in the image below, the equipotential lines surrounding a
1
positive point charge form concentric circles. Since the magnitude of the electric potential decreases as r with the distance from the
source, lines representing equal jumps in potential are spaced closer together nearer to the point source, and spaced farther apart
away from the point source. These concentric circles form because of the radial symmetry of the point source charge, and hence, the
radial symmetry of the field, suggested by equation (3) above. Since these lines represent points in space with equal electric potential,
there is no electric potential difference (ΔV = 0) between any two points on the same equipotential line. In a way, the map of
these equipotential lines can be thought of as a contour map similar to those of geographical elevation maps, in which points along
the same elevation line are at the same vertical elevation. Using this analogy, in which regions of higher electric potential correspond
to higher elevation, and regions of lower electric potential correspond to lower elevation, the direction of motion of a test charge in
an electric field now makes sense. A positive test charge moves from regions of higher electric potential toward regions of lower
electric potential, just as a ball moves from a region of higher elevation (top of a hill) toward a region of lower elevation (bottom of a
hill). Although we do not have a similar analogy for a negative test charge (since mass cannot be negative), we expect a negative
charge to behave in the reverse manner.
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The relationship between the electric field and the electric potential is clear when considering a single dimension. In the 1dimensional case, r
, so that: E ⃗ =
= x
1
4πε 0
Q
x
2
^
x
and V
=
1
Q
4πε 0
x
⃗ E = −
. Hence, the relationship between E ⃗ and V is:
dV
(4)
dx
In words, this relation means that the strength of the electric field at any point in space is the rate of change of the electric potential
over space. If the electric potential changes significantly over a small distance (as in the region near the point source in the image
above), the electric field is strong; if the electric potential changes only by a small amount over a large distance (as in the region far
away from the point source in the image above), the electric field is weak. (Thus, we say that the electric field is the gradient of the
electric potential.) Also, we note that the electric field lines always perpendicularly cross the equipotential lines, and that neither type
of field line can intersect another line of the same type. (This would imply that either the electric field points in two directions, or the
electric potential has two values, at a single point in space!)
In this laboratory experiment, we will explore these concepts by plotting the equipotential lines in the space between two different
charged electrodes (one positive and one negative). However, the configuration of the electric field lines and equipotential lines will
largely be determined by the shape of the sources of charge (the electrodes). Similarly, any symmetry present in the field lines will
correspond to the symmetry of the sources (the electrodes). The two common source charge configurations we will examine are the
parallel plate configuration (as present in parallel plate capacitors) and the dipole configuration (as present in electric dipoles).
Procedure
Each acetate sheet has a pattern of highly conductive silver-painted areas, with one electrode at each end, and a lattice of grid points
between them. Each sheet should be clipped onto the platform so that the metal clips contact the electrodes at each end. You should
connect each end of the platform to each terminal of the power source/battery using the banana-tipped wires. This will supply equal
and opposite charges to the electrodes, and maintain a constant electric potential difference between them. This potential difference
causes a current to flow through the resistive carbon film from one electrode to the other. By probing the area between the
electrodes with the digital voltmeter, you will be able to find sets of points having zero potential difference between them, i.e., they
lie on the same equipotential line. (In the 2-dimensional geometry of this experiment, the equipotentials are lines; in a 3-dimensional
system, they would be equipotential surfaces.)
Although there are technically an infinite number of equipotential lines between the electrodes, you will find and plot only the lines
which connect to the center grid points directly between the two electrodes (about 7 equipotential lines, from Row 3 to Row 9). Note
the numbered Rows and Columns of the grid points on each sheet for reference. With these equipotentials plotted, you will then
draw in the electric field lines for each configuration based on your expectations.
Parallel-plate charge configuration: Plotting equipotentials and electric field lines
To prepare the setup for data collection and plotting of the equipotential lines, do the following:
Slide the parallel-plate configuration sheet onto the platform (with the other conductive sheet beneath it for improved
conductivity), and connect the metal clips on the platform to the metal strips leading to the electrode at each end. Do not
place the photocopy of the charge configuration on top of the conductive sheets! Place it to the side on your lab
table, and record any measured values directly onto the appropriate location on the sheet.
Connect each terminal of the power source/battery to each end of the platform. (For consistency, the BLACK (negative)
terminal should be connected to the end of the sheet with the lowest Row numbers, while the RED (positive) terminal should
be connected to the end of the sheet with the highest Row numbers.)
Turn on the voltmeter, and set it to the 20 V scale. Connect the RED (positive) terminal of the voltmeter to the handheld
probe, and the BLACK (negative) terminal to the stationary probe with the attached base. (While the stationary probe is
placed at each center point on the grid between the electrodes, the handheld probe will be moved around to find points on
the map with zero potential difference, connecting to form the equipotential lines.)
Before finding the equipotentials, however, you must determine the voltage between the two electrodes. To do this, place the
stationary probe on the parallel plate electrode at the bottom of the grid, and place the handheld probe on the other parallel
plate electrode. If you can make a more precise measurement by increasing the sensitivity setting from 20 V to 2 V,
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you should do so; however, if you overload the voltmeter, it will display “1” and stop responding to increasing input
power. If this happens, you should decrease the sensitivity by returning to a higher setting. Record the voltage value
read by the voltmeter, with an uncertainty of about 5 mV. (This value should be approximately equal to your set voltage
source; if it is slightly less, then your connect may be bad, so adjust the setup to ensure maximal connection between
conductive surfaces!) Label the low and high voltage plates on your photocopy including the voltages on them, i.e., 0 V for
the low-voltage plate (connected via the BLACK lead), since we're defining the low-voltage plate as our reference, and your
recorded value from the voltmeter on the high-voltage plate (connected via the RED lead).
Next, you must find the voltage at each center point on the grid. With the stationary probe still placed on the bottom plate,
touch the handheld probe to the center dot in Row 9, Column 8. Record the voltmeter value for this point on your
photocopy. Move the handheld probe down to the grid point at Row 8, Column 8, and repeat the measurement, again
recording the value on your photocopy. Continue this process until you have recorded the voltage of every center point
between the parallel plates. Again, assume an uncertainty of 5 mV for your measurements.
Note: If the voltage value between your parallel plates is not close to your input voltage from the power supply/battery,
you should shift the conductive sheet slightly, as shown below, to improve the connection. If this still does not yield a
voltage near to your set input voltage, contact your lab instructor/TA and ask to switch to a different setup.
Now, you must find the equipotential lines that pass through each of these center points. To do this, place the stationary
probe onto the center grid point at Row 9, Column 8, and move the handheld probe around (left/right) of that point, finding
locations which have a potential difference of ΔV = 0 V with the center point. Mark these locations on your photocopy
with small X's. Be sure to check locations off to the side of the plates, to observe the behavior of the equipotentials
near the edge of the charge distribution!
Connect the marks with zero potential difference to form an equipotential line. You can make your job quicker/easier by
noting the symmetry of the charge distribution to predict what type of symmetry you'll see in your equipotential lines.
Repeat the previous 2 steps to obtain several more (7 total) equipotential lines between the parallel plates. Each time you
restart, place the stationary probe at the center point in Row 3-9, Column 8, and use the handheld probe to find points
around the grid with zero potential difference.
Outside of the region between the two plates, you should find that the equipotential lines are no longer parallel; rather,
they bend in a particular way. Why are the equipotential lines parallel between the plates but not parallel outside of the
plates?
Once you have drawn the equipotential lines on your photocopy, you should be able to sketch the electric field lines.
Remember that electric field lines begin at positive sources of charge and end at negative (or a reference) source charge. Also,
the electric field lines perpendicularly intersect the equipotential lines, and cannot ever cross one another! Be sure to include
some lines that may extend outside of the region between the two parallel plates. When beginning or terminating an electric
field line at a source charge, be sure that it is perpendicular to the electrode's surface because electrodes are equipotentials too.
(Metal plates are conductive, so that the charge within them is evenly spread out, and there is no difference in charge or
voltage between any two points along the plate!) Be sure to discuss in your lab report why these electrodes are equipotentials!
The lines you have drawn are, at least qualitatively, the electric field lines for the distribution of charge put on the parallel
plates by the power source/battery. Indicate with arrows how the electric field begins on areas with positive charge and ends
on areas with negative charge. A complete, labeled diagram (with legend included) should look similar to the example below:
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Parallel-plate charge configuration: Estimating electric field strength
The electric field E ⃗ in a uniform-field region between the two parallel plates can be calculated using the voltage difference,
δV = V2 − V1 , and the distance, δx = x 2 − x 1 , between two points between the plates on your photocopy. The points must
lie along the same electric field line, however, for the calculation to work. You can then approximate equation (4) above as:
E =
dV
dx
≈
δV
δx
by using discrete differences in voltage and distance.
To estimate the electric field strength, choose a region on your photocopy in which the electric field is uniform. This region should
be near the middle of the area between the two parallel plates, away from the edges. Indicate on your photocopy which two points
you use for this calculation, by circling them so that they're clearly distinguishable. Measure the distance δx between the points using
a meter stick, and estimate the uncertainty in this difference as 0.5mm (half of the smallest division). For the uncertainty in your
voltage values for each point, you should have used 5 mV, so that the uncertainty in the difference δV can be calculated using the
addition/subtraction rule (equation E.6) from the uncertainty guide. To find the uncertainty in the estimated value of E, you should
propagate the uncertainties in δV and δx using the multiplication/division rule (equation E.7) from the uncertainty guide. You
−−−−−−−−−−−−−
should find that:
σE
E
= √(
σ δV
δV
2
)
+ (
σ δx
δx
2
)
.
Electric dipole charge configuration: Plotting equipotentials and electric field lines
When you are finished with the above measurements, switch the conductive sheets so that the electric dipole configuration's
conductive sheet is on top, clipped to the platform as before. Just as the parallel plates were not infinitely thin, as required by an
“ideal” parallel plate configuration, the dipole configuration on the sheet is not ideal, and is considered a “physical” dipole due to its
finite size. Nonetheless, the results will be meaningful in the large region between the poles, so reconnect the circuit as before, and
begin collecting data:
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With the dipole sheet positioned on top of the parallel plates sheet on the platform, you will repeat the same procedure as
above for the previous configuration. First, determine the voltage between the two poles by placing the stationary probe at
the low-voltage pole, and placing the handheld probe at the other high-voltage pole. Record and label the voltages of each
plate onto the photocopy sheet, using the reading on the voltmeter and setting the low-voltage electrode at 0 V. Again,
assume an uncertainty of 5 mV.
Next, find the voltage value at each of the center points between the poles along the grid. Use the same process as before,
and record your voltage values onto the photocopy sheet, off to the side of each row whose point you're testing.
Find and plot the equipotential lines for the electric dipole configuration using the same method as was used for the parallel
plate configuration. Place the stationary probe on a center point, and find other locations yielding a 0 V potential difference
with the center point, mark these locations on the photocopy, and connect them. Be careful: Unlike the parallel plate
configuration, the electric dipole does not produce mostly uniform straight field lines. Rather, most of them are
curved.
For your lab report, you should consider the differences between these lines and those of the parallel plate charge
distribution. Why do they look different? Are any of these equipotentials straight, or are they all curved? Why? Consider
the symmetry of the source charge configuration of each case, and how it might determine the symmetry and shape of any
of the field lines!
Finally, draw in the electric field lines corresponding to these 7 equipotential lines, produced by the electric dipole source
charge configuration. Be sure to distinguish your electric field lines from your equipotential lines using a legend, and place
arrows on the electric field lines to indicate their direction. Your complete diagram should look similar to the example below:
Questions
In your lab report, you should write meaningful explanations for any similarities or differences between the field line configurations
for the two charge distributions, considering the relevant physics theory for this lab. Despite the minimal quantitative data analysis
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required for this experiment, you should have plenty to say about your qualitative results. Additionally, you should include
explanations for the following questions:
1. Why are the electrodes considered as equipotentials?
2. What does the density of the electric field lines imply about the electric field strength?
3. How are the electric field lines oriented relative to the equipotential lines? Why?
4. For the parallel plate configuration, what happens to the electric field lines and equipotential lines at the edges of the source
charge distribution?
5. For the electric dipole configuration, are any of the equipotential lines straight? Why or why not?
6. For the electric dipole configuration, what would the electric field between the two poles look like if we swapped out the
negative pole for another positive pole? Draw a sketch of what the electric field lines would look like for this new
configuration.
7. For the electric dipole configuration, where is the electric field strength greatest?
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