Experiment #{Experiment Title}Date Performed .docx

Experiment #
{Experiment Title}
Date Performed:
Date Report Submitted:
Report Author:
Lab Partner[s]:
Instructor’s Name:
Section Number:
I. Introduction
Three sentences are fine for the introduction. State what you
measured, what you calculated, and what you are comparing
your results to. Avoid using first person in the report. This
section is 5 points. Refer to Appendix B and your Lab 1 Report
for full instructions.
II. Data
This section is worth 20 points.
All measurements must be included and have proper unites and
significant figures.
Data needs to be neat and understandable with explanations or
equations.
Put in-lab data sheets signed behind this page when submitting

the paper copy of your report.
The “data” heading can stay on the same page as the
introduction or be hand written on top of the data sheet.
Refer to Appendix B and your Lab 1 Report for full instructions
and how to achieve full points.
III. Data Analysis
This section is worth 30 points. It contains the calculations,
graphs, and sample calculations if one was performed
repeatedly. Always calculate a percent difference between
experimental and theoretical vales. There are directions on how
to set up graphs in Appendix B.
You can use Word to type equations by clicking
“Equation” on the “Insert” Tab or by clicking Alt and =
simultaneously. Word lets you use Latex or Unicode to type
equations. It also has buttons to press to insert symbols under
the new “Design” tab if you do not know Latex or Unicode. If
you hover over button, it will tell you how to type it using
Latex or Unicode (whatever is selected)
The hypotenuse length can be found using the side lengths:
Refer to Appendix B and your Lab 1 Report for full instructions
and how to achieve full points.
IV. Discussion
This section will contain a table of summary results and
paragraphs discussing the accuracy of results, the sources of
errors, and the physics or answers to questions. Below is a
sample summary table. Please be sure to update it or replace it
with a table for the correct information.
Table 1 : Summary of Results
Measured Diameter [m]
Error in Measured

Theoretical Diameter [m]
%Difference
It is important to discuss types of error and largest error in your
experiment. Refer to Section D of Appendix B and the
Discussion from Lab 1 for more information.
V. Conclusion
You only need two sentences minimum and this section is worth
5 points. Refer to Appendix B and your Lab 1 Report for full
instructions and how to achieve full points.
2
Experiment 2
Electric Potential and Field Mapping
Introduction
In this experiment, you use a voltage probe and a computer
data acquisition system to
measure the electric potential between two metal electrodes.
The electrodes are placed in a tray,
which contains a shallow layer of water. The electrodes are
connected to a D.C. power supply,

which maintains a constant potential difference. The water
allows an electric current to flow
from the positive electrode to the negative electrode. See
Figure 1.
After measuring the electric potential surrounding the
electrodes, you will transfer these
numbers to an Excel spreadsheet. There you will produce
surface plots of the electric potential.
For one particular arrangement of electrodes, you will also use a
digital multimeter to measure
the potential difference between two closely spaced points in
the water. This will allow you to
calculate the strength of the electric field between these points.
These electric field strengths,
and the location of the corresponding points, will then be
graphed to test Gauss’ Law. All
results are displayed graphically, and the data sheets constitute
the data and nearly all of the
data analysis for the report. Spend time adding labels and
color-codes to your data sheets.
Though a large amount of numerical data will be recorded and
graphed, the results of this
experiment are largely qualitative. Therefore, a quantitative
error analysis is not required for
this experiment’s report.
!
Figure 1. The apparatus set up with two parallel plates.
Concept
Suppose a charged test particle is brought near other
electrically charged objects. In the
experiment, the test particle is the tip of a metal probe placed in

the layer of water and the
other charged objects are the electrodes. In this case, the test
particle experiences a force of
attraction or repulsion depending upon the sign of the electrodes
(positive or negative).
One way of depicting the influence of electrically charged
objects is by examining the
energy a charged test particle will gain or lose when it is moved
around in the neighborhood of
the main charged objects. One must push against a force of
repulsion to move a positively
charged test particle toward a positive electrode. This force,
multiplied by the distance the test
particle is moved is the amount of work required to move the
particle. In the experiment, you
CURRENT VOLTS
0.00 10.00
data acquisition:
Vernier Lab Pro
AC/DC
Adapter
2 - �3
won't actually feel the repulsive force. It is far too small to
experience tactilely. However, the
data acquisition probe and the digital multimeter measure the
energy (per unit charge) of free
charge in the probe tip. This energy per unit charge (Joule/
Coulomb) is called electric

potential. The difference in the electric potential at two
different locations is called potential
difference or the more commonly voltage. Hence 1
Joule/Coulomb = 1 Volt.
!
Figure 2. Electric field lines of a dipole located at the origin.
Drawn in Grapher as r = cos2θ.
� ! !
Eqn. (1) (2) (3)
The electric field is the electrostatic force exerted on a charged
test particle per unit of
charge on the test particle. See Eqn. (1). The electrostatic
force is the Coulomb’s Law force
produced by a nearby charged object. q is the charge of the test
particle. The electric field has
units of Newtons / Coulomb.
The total electric potential difference is computed by adding all
of the individual
amounts of work (energy) used to move this charge against the
force of the electric field from
one point to another. Work done by an electric force is defined
as the scalar (or dot) product of
the distance the test particle moves and the electrostatic force.
See Eqn. (4). By dividing Eqn.
(4) by the charge, q, and using Eqns. (1) and (3) we obtain Eqn.
(5). When, the field is uniform
over a small distance, Eqn. (5) reduces to (6).
! ! !
Eqn. (4) (5) (6)

!
E =
!
F
q
V =
W
q
ΔV =
ΔW
q
W =
!
F id
!
l∫ V =
!
E id
!
l∫ ΔV =
!
E iΔ
!
l
2 - �4

If ! and the electric field are perpendicular to one another,
then the dot product of
these two vectors is zero. Then there is no change in potential
along a path perpendicular to
the direction of the electric field. This path is an equipotential
since all points along this path
have equal potentials. To conclude, field lines are always
perpendicular to equipotential lines.
It also stands to reason; the electric field should be strongest
where the equipotential
lines are most dense. The geometry of the charged object also
affects how the electric field
varies with distance from the object. Eqn. (6) is a valid
approximation if the field doesn’t
change over small distances.
Just as a marble or ball rolls down hill due to gravity, an
unbound, charged test particle
will move to a region of lower electric potential. In this way,
an analogy can be drawn between
electrostatics and gravitation. This analogy is exact due to the
similarities between Newton’s
Law of Gravity and Coulomb’s Law. Here, the electric field is
analogous to the gravitational
field g. Geographic contour lines are lines of constant elevation
above mean sea level. In this
experiment, equipotentials are lines of constant potential above
ground potential, which is
defined as V = 0.
Gauss’ Law allows us to derive expressions, which describe the
geometry of the electric

field for a given distribution of charged particles. Two charge
distributions of practical interest
are the long, charged line and the charged, infinite sheet. These
have practical use since charged
metal sheets are used to build capacitors, and long charged lines
are the basis for electrical
current in wires.
! (7)
If the linear charge density is λ, and for a point a radius r from
the line, the electric field
is given by Eqn. (7). Consult your textbook to see how this
equation is derived from Gauss’
Law. Figure 3 is a two-dimensional slice of this particular
three-dimensional electric field.
Hence, Eqn. (7) implies the magnitude of the electric field is
proportional to 1/r.
From Eqn. (5) it is seen that the electric potential is related to
the electric field by an
integral. By the same token, the electric field is the spatial
derivative of the electric potential
(multiplied by -1). This has an important interpretation in the
gravitational analogy to electric
fields. Since a derivative is the slope of a tangent line, the
electric field can be visualized as the
slope (or gradient) of a potential surface.
Method
The HY3003D power supply is capable of delivering precise,
constant currents or
constant voltages. The default mode is constant current.
However, we usually want a power
supply to operate in the constant voltage mode. This requires

setting a maximum limit for the
current. Since the fuses in the digital multimeters are rated to
400 mA, we conservatively set
the current limit to 0.3 Amps. (In some experiments, we use
larger currents and then use the 10
Amp jack on the multimeters.)
!
E =
1
2πε
0
1
r
r̂
2 - �5
1) With the power supply OFF, turn all current and voltage
knobs to their lowest (most
counter-clockwise) setting. Also make certain the push-button
labeled “AMPS” is
pressed IN.
2) Turn the power supply ON before connecting any wires.
3) To set the current limit, connect one wire (a short) between
the power supply’s red and
black jacks. The black and green jacks are common due to a
connecting metal strap.

4) Turn the COARSE voltage knob clockwise about 1/10th of a
revolution. The red light
labeled “CC” should be illuminated.
5) Increase the COARSE and FINE current knobs to 0.3 Amps.
This sets the current
limit.
6) Disconnect the wire between the red and black jacks. The
“CC” light should go out and
the green indicator light labeled “CV” should illuminate.
7) The power supply is now ready to be used in a constant
voltage mode. Use the
COARSE and FINE voltage knobs to apply the desired voltage.
8) Lower all voltage and current knobs to zero when you are
finished.
9) Disconnect all wires before turning the supply OFF.
10) When coils of wire are connected to this power supply,
adjust the voltage and current
slowly to avoid a back-EMF that might cause damage.
Procedure
Part 1 Potential Between Parallel Charged Plates
1) Turn on the table’s power strip and then the D.C. power
supply and the computer. The
computer’s ON button is on the back of the iMac in the lower
left corner
2) Place a laminated graph paper grid into the yellow tray and
then place two aluminum
bars on top of the graph paper. Pour a thin layer of tap water

into the tray. Use
enough to completely surround the electrodes and cover the
entire sheet of graph paper
but not enough to submerge the electrodes. Return the tray to
your station and dry any
spills with paper towel.
3) Connect the voltage probe to one of the analog channels
labeled CH 1, CH 2, etc. Start
the data acquisition program Logger Pro and Microsoft Excel.
Ideally, Logger Pro will
automatically recognize that a voltage probe is connected. If it
does not execute the
following pull-down menu commands. Experiment > Set Up
Sensor > Show All
Interfaces. Then click on the channel the voltage probe is
plugged into. As you click
and hold down the mouse button, execute these commands:
Choose Sensor >
Voltage > Voltage (+ / - 10V).
4) Test to see if the data acquisition unit is working correctly by
connecting the voltage
probe’s black plug to ground and the red one to the power
supply’s 5 V output (middle
two banana jacks). The live readouts in the screen’s lower left
corner should give very
close to 5.0 V. If random or nonsensical voltages are displayed
try replacing the voltage
probe. The solder joints under the electrical tape sometimes
break. Disconnect the
voltage probe after this test.
2 - �6

5) Also, execute these commands: Experiment > Data
Collection… and set the Mode
to Selected Events. This allows you to collect and save
voltages. Close the last
dialog box and then click the collect button (the triangle in the
green rectangle) to begin
data acquisition. Save each datum by clicking the light blue
circular icon next to the
collect button. You can delete the graph window in Logger Pro
since it will not be useful
in this experiment. Avoid mistakes by collecting one column of
data at a time from the
plastic tray and then copying and pasting into Excel (see details
below).
6) Starting in 2013, we are using power supplies that contain
more sophisticated circuitry
and require greater care in their use. Students and instructors
must consult the method
section on the use of the HY3003D power supplies. Connect the
power supply and
electrodes as shown in Figure 1. In Fig. 1, heavier lines
represent black wires, which
connect to the power supply’s ground (zero Volts) jack. Lighter
lines represent red wires,
which connect to the power supply’s red jack. The same
convention is used for the wire
leading from the data acquisition board and the (ideally red)
multimeter probe with its
single prong. In this way, the data acquisition system measures
and records the
potential at the tip of the probe relative to zero Volts on the
power supply. The black
wire from the measuring device to the power supply’s ground
establishes that the power

supply’s ground is your reference zero. Note that this
convention as to heavy and dark
lines is not continued in other figures in this manual.
7) The graph paper in the bottom of the tray is marked off every
two centimeters. Measure
the potential at every “+” symbol on the graph paper. When the
electrodes obscure the
marks, touch the probe to the electrode at the desired location.
Be sure to collect data
near and all the way around the plates.
8) Do not apply more than 5 Volts to the electrodes. The data
acquisition board is limited
to 5.12 Volts (512 is a power of two). Do not allow the
positive and negative electrodes
to touch. This causes a spark and overloads the power supply!
9) After recording one column of data, click the red stop button
and then click on the
“Potential” column heading in Logger Pro to select the entire
column of values. Execute
the Copy command in the Edit menu and then click on the green
Excel icon in the
Dock to switch to Excel. With a blank spreadsheet open, use
the Paste Special…
command in the Edit menu to transfer the potentials from
Logger Pro. Click on the
Text radio button and click OK. These procedures adjust for a
mismatch between the
clipboard Logger Pro writes to and the default Excel clipboard.
10) Within Excel, arrange the numbers in columns and rows,
just as the electrodes are
arranged in the tray. This will create a one-to-one map of what
is in the tray. Now is a

good time to save the spreadsheet to the hard disk. Please
locate the file on the desktop
and delete it at the end of the lab period. Once finished, you
will have created a scalar
field of electric potential values. Insert column and row
headings above and to the left of
the array of voltages. Use integers that represent the distance
(in cm) along the grid
paper.
2 - �7
11) Plot a surface graph of the electric potential in Excel.
a) Select the array of data including the column and row
headings. Then click the
Insert menu and select Chart > Surface. Here, the z-coordinate
represents the
electric potential; x and y represent the spatial coordinates in
the tray.
b) Use the Add Chart Element button on the far left of the Chart
Design ribbon to
enter a graph title and axes labels. You must select the axis
before adding the label.
c) Print a copy of the graph for each lab partner. Questions:
What does theory
predict for the shape of the potential surface between two
parallel plates?
Qualitatively, does your data agree with theory? How can you
use the graph to find
the electric field strength between the plates? Explain in your
discussion section.

Use Eqn. 6 to calculate this electric field from your graph.
Part 2 Potential Around a Charged Line
1) Disconnect and remove the parallel plates. Build the
arrangement of electrodes in Fig. 3.
Connect the wires to the ring and rod using alligator clips (the
ring connects to the
black, ground terminal on the power supply). Place the rod in
the water at the center of
the ring. Connect the black wire from the data acquisition
board to the power supply’s
ground.
!
Figure 3. Two-dimensional slice of a long, charged line
2) Again, use the data acquisition equipment to measure the
potential at each + symbol in
the tray. Include the potential on the ring and the rod. Produce
a surface plot of the
data. Insert titles and axes labels and delete the legend.
3) Produce a second surface plot of the data and then execute
Chart Design, then
Change Chart Type from 3-D Surface to Contour. Again, add a
title and axes
labels.
4) Print copies of your data table and graphs for each lab
partner.
5) Question: What is the mathematical shape of the electric
potential surface for Part 2?
To answer this question, assume Eqn. (7) is correct and use
Eqn. (5) to derive an

expression for the radial dependence of the electric potential
around a charged line.
Include this derivation in the data analysis section of your
report. As stated in
CURRENT VOLTS
0.00 10.00
2 - �8
Appendix B, the report is more readable if you write equations
by hand instead of using
text (such as x-squared or x^2). This also eliminates the time
necessary to use an
equation editor.
Part 3 Field Around a Charged Line
1) Disconnect the computer data acquisition probe and set it
aside. Also quit Logger Pro.
Obtain a digital multimeter and a two-pronged probe from the
front table. Connect a
red wire from the meter’s (+) jack to the red jack of the two-
prong probe. Connect a
black wire between the meter’s COM jack and the black jack of
the two-prong probe. In
this way, the meter measures the electric potential at the tip of
the red probe relative to
the tip of the black probe (no longer relative to the power
supply’s ground). See Fig. 4.
!
Fig. 4. Set-up for Part 3.

2) Using Vernier calipers, measure and record the distance, Δl,
between the two prongs of
the probe. Raise the voltage on the power supply to between 10
and 20 Volts. If you
don’t recall how to read the Vernier Caliper, see Appendix H.
3) Move the probe so both prongs touch the ring and then the
rod. Next, probe a few
spots in the water. Twist the two-prong probe in the water,
about the vertical axis and
examine the voltage on the meter.
4) Find the orientation of the two prongs inside the ring, which
produces the smallest (near
zero) voltage reading. Record this value and make a sketch of
the orientation of the
probes relative to the electrodes. Draw a short line between the
two probe points in your
sketch. Question: What electrical quantity does this line
represent? Find the
orientation of the two prongs, which produces the largest,
positive voltage reading. Draw
this line on the sketch and record the voltage. Questions: How
does this orientation
relate to the direction of the first line? What electrical quantity
does this line represent?
5) Use the two-prong probe to measure ΔV at seven points
inside of the ring, but at radii of
2, 3, and 4 … centimeters out from the center of the ring.
Locate the midpoint between
the two prongs at these radii. Record the radii and the voltages
in a table, then use
Eqn. (6) to calculate the electric field.
6) Measure the electric field outside the ring. Questions: Does

this agree with your
knowledge of electrostatics? Why does the electric field have
this value?
CURRENT VOLTS
0.00 10.00
2 - �9
7) Plot a graph of electric field strength versus 1 / r to verify
the functional dependence
seen in Eqn. 7. In Excel, choose a scatter chart type and then
fit the points with a
straight line. Check the appropriate box so the R-squared value
is displayed. Print a
copy of the data and graph for you and your partner.
Questions for the Discussion
1) What two slightly different quantities do Eqns. (2) and (3)
refer to?
2) Write a short paragraph describing the relationship between
equipotential lines and
electric field lines as well as the relationship between field
vector diagrams and field line
diagrams.
3) What are the sources of experimental error, and which was
largest? What categories do
these errors fall into? Error can be intrinsic to the quantity
itself or found in the
measuring procedure or the tool used. Intrinsic means the
quantity being measured has

some variability built into it by nature. This error is
unavoidable no matter how precise
the measuring tool. Error in measurement usually refers to the
precision of the tool you
are using.
2 - �10
PHY 2092 Distance Learning Experiment Guide
02 Electric Potential and Field Mapping
YouTube Video #1
This 7:56 video is another fun one that is packed with excellent
visualization aids and a good, accurate
narration.
https://www.youtube.com/watch?v=Y6YdC2UoDYY
Photographs
Examine all photographs in the alphabetical filename order
given. Again, they can be found in Canvas >
Files > Experiments > 02 Potential and Field. The experiment
description found in the lab manual has
been updated with color-coded diagrams for this term. It also
includes an additional diagram for Part 3.
Videos
As with experiment 01, these videos are located in Canvas >
Panopto Recordings > Exp 02 Potential and
Field. Most of these files are very large. Therefore, streaming
and watching them may be preferable to

downloading. This situation is the result of external constraints
placed on the timeline for recording the
videos. Notify your GSA if the file size becomes a problem.
Unfortunately, an important video segment was not recorded
during this aforementioned timeline. One
must imagine the dual-pronged probe being twisted about a
vertical axis while it is contact with the water.
The digital multimeter’s (DMM) voltage reading will change
rapidly. We use Melbourne city water for this
experiment and its mineral content causes the voltage measured
by the DMM to fluctuate. However,
these fluctuations are small (a few 1/100ths of a Volt) compared
to the effect of twisting the probe (several
tenths of a volt). To assist with your answering the questions in
Part 3, procedure 4: consider this
additional question: When the prongs of this probe are parallel
to a field line, the angle between � and
� in Equation 5 will be either zero or 180 degrees. When is it
zero and when is it 180 degrees?
�
Δ
!
l!
E
0 1 2 3 4 5 6 7 8 9
0
1
2

3
4
5
6
7
8
9
The arrows represent the prongs of the
dual-pronged probe. If the left probe is
connected to the meterʼs positive terminal,
then the meter will read a positive number
because the electric potential at the left
probe is higher than the potential at the
right probe.
A graph of electric potential of charged point
particle versus radial distance from that
particle: V(r) = 1 / r. The particle sits at the
origin. The y-axis is electric potential V and the
x-axis is the radial coordinate, r.
https://www.youtube.com/watch?v=Y6YdC2UoDYY
Data
The data for all parts of this experiment are contained in one
Excel spreadsheet. It is found in Canvas >

Files > Experiments > 02 Potential and Field > Exp 02
Data.xlsx.
Unlike the previous experiment, there is a great deal of physics
contained in this experiment. Students
should pay special attention to the questions listed in the
procedure.
Sheet1Part 1: Potential between charged, parallel plates
(V)Probe Coordinates
(cm)02468101214161820141.651.882.182.442.722.963.233.553.
794.134.43121.491.722.082.362.672.993.283.553.874.204.5510
1.421.651.972.322.642.933.283.613.934.254.5981.411.641.992.
292.683.003.333.653.974.294.6061.401.651.962.282.523.063.35
3.653.974.254.6041.411.692.022.302.523.043.333.633.954.214.
5621.441.082.052.352.502.963.273.543.904.184.5601.501.822.1
12.402.572.953.233.513.804.124.52Part 2: Potential around
charged line (V)Probe Coordinates
(cm)02468101214161820200.000.000.000.001.221.211.300.000.
000.000.00180.000.001.211.311.371.401.521.431.320.000.0016
0.001.201.311.451.571.631.721.621.461.260.00140.001.271.421
.621.851.992.011.821.581.400.00121.161.371.531.832.302.652.
421.991.671.451.18101.191.361.571.922.674.662.742.081.701.4
61.2181.191.341.521.822.282.752.391.961.641.431.1860.001.26
1.431.641.872.071.951.761.521.330.0040.001.181.291.451.581.
721.661.521.371.210.0020.000.001.161.241.351.481.431.351.22
0.000.0000.000.000.000.001.161.281.240.000.000.000.00Part 3:
Potenial difference between charged line and grounded ring
(V)Δl (cm)1.3ΔV outsidelowest potential (V)0.03of ring
(V)highest potential (V)1.010.01radius r (cm)ΔV
(V)22.0831.3841.0650.8660.7070.5980.54by B.H. and B.C.

Experiment #{Experiment Title}Date Performed .docx

Experiment #{Experiment Title}Date Performed .docx

Recommended

Recommended

More Related Content

Similar to Experiment #{Experiment Title}Date Performed .docx

Similar to Experiment #{Experiment Title}Date Performed .docx (20)

More from rhetttrevannion

More from rhetttrevannion (20)

Recently uploaded

Recently uploaded (20)

Experiment #{Experiment Title}Date Performed .docx