Electric Fields
Exploration of electric potential and electric force, with application to gel electrophoresis.
1
CONTENTS
Objectives ............................................................................................................................................. 1
1.1
Experimental Goal ........................................................................................................................ 1
1.2
Prerequisite skills and Knowledge ................................................................................................ 1
1.3
Research Skills .............................................................................................................................. 1
1.4
Learning Objectives ...................................................................................................................... 2
2
Pre-Experiment Assignment ................................................................................................................. 2
2.1.1
Phet Practice.......................................................................................................................... 3
2.1.2
Equipotential Lines and Electric Field Lines ........................................................................ 3
2.2
3
Prepare for the Experiment ........................................................................................................... 4
Laboratory Manual................................................................................................................................ 5
3.1
Materials Check Off List............................................................................................................... 5
3.2
Safety and Waste Disposal Protocols............................................................................................ 5
3.3
Experimental Procedure ................................................................................................................ 5
3.3.1
Prepare Electrolyte Solution ................................................................................................. 5
3.3.2
Electrolytic Tank Method for Mapping Equipotentials ........................................................ 5
3.3.3
Mapping the Equipotential Lines between Two Charged Points .......................................... 6
3.3.4
Mapping the Equipotential Lines in a Gel Electrophoresis Cell ........................................... 8
3.3.5
Analysis................................................................................................................................. 8
3.4
Post-Lab Assignment .................................................................................................................... 8
1
1.1
OBJECTIVES
EXPERIMENTAL GOAL
Students will measure equipotential lines for two simple electrode configurations in order to determine
the electric field for each configuration.
1.2
PREREQUISITE SKILLS AND KNOWLEDGE
Students should be familiar with vectors and have an understanding of the relationship between force,
work, and potential energy.
1.3
RESEARCH SKILLS
After this lab, students will have had practice in:
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•
•
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1.4
Mapping equipotential lines
Drawing electric field lines from equipotentials
Building simple electrical circuits
Using LabVIEW
LEARNING OBJECTIVES
After this lab, students will be able to:
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•
•
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Describe the basic structure of an electric field.
Predict the shape of an electric field resulting from a given electrode configuration.
Predict the effect an electric field will have on charged particles
Determine the electric field from equipotential lines
2
PRE-EXPERIMENT ASSIGNMENT
In this experiment you will map the electric fields and equipotential lines in two simple electrode
geometries:
1. Two point charges:
2. Two charged parallel lines
What do you think would happen to a positively charged particle (like a proton) if it were placed
somewhere between the two point charges? Between the two charged lines? 1
Equipotential lines are a lot like contour lines on a topographic map, except that where lines on a
topographic map indicate the same height above sea level, all points on one equipotential line have the
same electrical potential. *
Match up the following three topographic maps with the three side views of the hills they might
represent: 2
*
For more information about contour lines go to the USDS USDS Natural Resources Conservation
Service publication, “Reading Topographic Maps” for a quick tutorial on how to read a topographic map.
You can find this publication in the lab folder under the Student Resources tab on e-Learning.
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Electric Fields |3
The spacing of contour lines is an indicator of how rapidly the energy (potential or kinetic) of an object is
changing as it crosses them. Since the rate of change of its potential energy, U, with respect to position is
the force felt by the object,
𝐹𝐹(𝑥𝑥) = − 𝑑𝑑𝑑𝑑�𝑑𝑑𝑑𝑑
(1)
the contour lines on a map help us to predict the force felt by an object at any point on the map.
2.1.1
Phet Practice
Go to the Phet simulation of charges and fields:
http://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html
Try these things:
1. Arrange the charges to reproduce the two charge configurations described above.
2. Draw equipotential lines using the equipotential tool. Be careful to keep the contour interval the same,
or as close as possible to the same. Hint: it is easier to control the voltage on the equipotential tool
when the slope is not steep.
3. Use the E-Field Sensors to probe the magnitude and direction of the electric field at different
locations within each configuration.
Discover the answers to these questions about the electric field caused by two opposite point charges:
At which location(s) is the electric field strongest? 3
At which location(s) is the electric field weakest?4
How do the equipotential lines relate to the electric field lines? 5
Also answer these questions about the electric field caused by two parallel wires of opposite charge:
Where is the electric force the strongest?
What is the difference between electric field lines directly between the wires and those outside the wires?
2.1.2
Equipotential Lines and Electric Field Lines
Charged particles exert a force on each other. Coulomb’s law relates the electrostatic force, F, exerted on
each particle to the charges, q1 and q2, of the particles and the distance between them:
(2)
𝐹𝐹 = 𝑘𝑘
𝑞𝑞1 𝑞𝑞2
𝑟𝑟 2
𝑟𝑟
In Equation (1), r is the unit vector along the axis extending through the two particles, and k is the
electrostatic constant. An electric field is a vector field, made up of vectors at each point around the
charged object. The electric field at each point is the force per unit charge exerted on a test charge, q0, at
that point.
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𝐸𝐸 = 𝐹𝐹�𝑞𝑞0
(3)
What are the units of the electric field? 6
In SI base units, a newton (N) is kg·m/s2 and a coulomb (C) is A·s. Use dimensional analysis to write the
units of the electric field in terms of volts (V = (kg·m2)/(A·s3)). 7
We draw electric field lines to indicate the electric field near a charged object. Field lines show the
direction of the force that a positive test charge experiences in the field at each point. Field lines are also
used to show the magnitude of the electric field; the higher the density of field lines the greater the
magnitude of the electric field strength, E.
It is much easier to measure electrical potential than to measure electric fields. Electric potential is a
scalar quantity that can be measured with a voltmeter. The potential difference between two points in an
electric field is the work per unit charge, dW, done on a charge in moving it from one point to another
against the electric field. If the distance between the two points is ds, the change in the electric potential,
dV, is:
(4)
The the scalar product is
(5)
𝑑𝑑𝑑𝑑 = −
∆𝑊𝑊
𝑞𝑞
𝐹𝐹
= − · 𝑑𝑑𝑑𝑑 = −𝐸𝐸 · 𝑑𝑑𝑑𝑑
𝑞𝑞
𝐸𝐸 · 𝑑𝑑𝑑𝑑 = 𝐸𝐸𝑠𝑠 𝑑𝑑𝑑𝑑
where 𝐸𝐸𝑠𝑠 is the component of E in the direction of s. Thus, the component of the electric field along a
specified axis is given by:
(6)
𝐸𝐸𝑠𝑠 = −
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
This equation says that the component of the electric field, E, in any direction, s, is the rate of change of
the potential with respect to distance in that direction.
The SI units of the electric field are newtons per coulomb (N/C) and those of potential difference are
joules per coulomb (J/C). Potential differences as read on a voltmeter are in volts, where a volt is defined
as 1 volt = 1 joule / coulomb.
2.2
PREPARE FOR THE EXPERIMENT
Read through the experiment so that you can prepare your lab notebook. When you feel ready, test your
preparation with the Pre-Experiment Quiz on e-Learning.
Determine what your VI will need to do, and make it. Send it to yourself in an email.
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3
3.1
LABORATORY MANUAL
MATERIALS CHECK OFF LIST
Each small group of (2-3) students will have:
1 laptop computer with LabVIEW
SensorDAQ with associated voltmeter
DC power supply, either variable or fixed
100 mL volumetric flask
Scoopula
Large (140 mm diameter) glass petri dish
Gel electrophoresis cell
250 mL Erlenmeyer flask
3 banana plug leads
2 alligator clips
2 steel nails
Ring stand
1 ring stand bar
3 ring stand clamps
Disposables (please follow waste disposal instructions):
Weighing boat
Sandpaper or steel wool
4 sheets grid paper
Paper towels
3.2
SAFETY AND WASTE DISPOSAL PROTOCOLS
Weighing boats must be disposed of in the benchtop Lab Waste container. Used electrolyte solutions may
be poured down the drain. Clean up spills immediately.
3.3
3.3.1
EXPERIMENTAL PROCEDURE
Prepare Electrolyte Solution
Obtain from your instructor, or the container, the molar mass of the sodium acetate salt you are using.
Prepare 100 mL of 0.5 M sodium acetate solution, using the volumetric flask and Erlenmeyer flask. Refer
to your lab notebook for more details.
3.3.2
Electrolytic Tank Method for Mapping Equipotentials
You will use an electrolytic tank to provide the weak conducting material that is helpful for the mapping
of equipotential curves. In this system, the electrodes are immersed in a shallow pool of dilute electrolyte
solution. One probe of the voltmeter is connected to one electrode and the other probe measures potentials
at various points in the solution.
The pool is a large glass petri dish resting on a sheet of grid paper. Confirm that your petri dish is clean,
dry, and intact.
1. Label the axes of your grid paper to allow you to plot your data later.
2. Place your petri dish on the paper, mark the location on the grid paper, and label the gridlines.
Placing the petri dish in the corner of the grid paper may make it easier to match up gridlines.
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3. Mark the location of the dish on a second piece of grid paper. This is the sheet on which you will
record your measured potentials.
Figure 1. Ring stand assembly.
3.3.3
Mapping the Equipotential Lines between Two Charged Points
First you will map the equipotentials in the electric field between the tips of two nails.
Begin with your power supply disconnected, or with the switch open.
1. Center a nail head in each of the alligator clips and suspend them so the nails are perpendicular to the
bottom of the petri dish, with the tips just short of touching the bottom. Use the ring stand bars and
clamps to make an assembly similar to the one in Figure 1. Be careful not to scratch the surface of the
glass with the nail.
2. Choose a distance between nails that
allows you to measure both the
potential change between the nails
and outside the nails.
3. Record the position of your
electrodes (nails) on the recording
grid.
4. Connect the positive output of your
power supply to one of the alligator
clips. Connect the negative output
from the power supply to the other
alligator clip.
5. Use the third banana lead to connect
the ground lead of your voltmeter to
the negative output of your power
supply.
6. The positive (red) end of your
voltmeter will be your potential
probe.
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7. Pour approximately 100 mL of electrolyte solution into the petri dish. The nail tips should be 1 – 2
mm submerged.
8. Turn on the power supply and turn the current knob a little less than a quarter turn. Turn the voltage
knob until the power supply shows 6.0 V. The current is very small and may not show on the power
supply screen, but you may see bubbles starting to form on one of the nail tips.
Q1. What should the potential probe read at the positive electrode? 8
Q2. What should the potential probe read at the negative electrode? 9
Check to make sure your predictions are true. If not, check with your instructor, to make sure your
connections and reasoning are both correct.
9. Now use your probe to explore the potential near the positive electrode.
Q3. What happens to the voltage as you move away from the positive electrode? 10
Read through the steps 11 -15 and the suggestions for best results before starting to record potentials.
Work with your partner so that one partner moves the potential probe while the other records potentials.
You will be mapping the lines along which the potential is equal.
10.
11.
12.
13.
14.
Start at a point near the positive electrode.
Record the position by marking a spot on the recording grid.
Record the magnitude of the potential.
Move the probe until you find a different spot with the same potential. Record that spot.
When you have enough spots to draw an accurate curve, move farther away from the electrode and
look for a spot with a potential 0.20 V or 0.30 V different from your first equipotential. Start a new
equipotential curve by repeating steps 10 – 13.
Use the above instructions to map 3-4 equipotential lines between 3V and 5V.
Q4. Hypothesize how the equipotential lines will look on the other side of the dish.
Map 3-4 equipotential lines between 0V and 3V.
Q5. Was your hypothesis correct? If your finding deviated from your hypothesis, what did you
discover?
Suggestions for best results:
1. Work mostly on the side of the dish closest to you.
2. Record equipotential lines with a constant interval between them. Recommended intervals: 0.20 V, or
0.30 V.
3. Hunt for equipotential points by running the probe along the thicker grid lines.
4. Don’t assume the symmetry of the contours. Test your assumption with a few points.
5. Avoid bumping the dish.
When you have recorded 6 – 8 equipotential lines, turn off the DC power supply and turn the current and
voltage knobs to zero.
3.3.3.1 Clean Up Petri Dish Assembly
1. Raise the assembly that holds the nails and pour the electrolyte solution from the dish into a waste
container, or down the drain.
2. Rinse and dry the petri dish.
3. Disconnect the nails from the alligator clips, clean them and put them into the dish.
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3.3.4
Mapping the Equipotential Lines in a Gel Electrophoresis Cell
1. Place the gel electrophoresis cell onto a new measuring grid and mark the location. Also mark the
location of the cell on a new recording grid. You may wish to draw both a top view and a side view.
2. Pour electrolyte solution into the cell until the level is about 5 mm above the central platform.
3. Use the alligator clips to connect the negative lead to the banana plug on the black side of the
electrophoresis cell and the positive lead to the banana plug on the red side.
4. Your voltmeter should already be connected as before.
5. Turn on the DC power supply, turn the current knob about a quarter turn and set the voltage to 8.0 V.
6. Check to make sure your electrodes have the voltages you expect.
7. Explore the potential landscape.
8. When you are done, open the switch and disassemble your circuit to the components you started with.
Q6. What happens to the voltage as you move the probe away from the positive electrode? How is this
voltage change different from the change you observed in the petri dish?
Q7. Describe how the potential varies with depth.
9. Map the equipotential lines between the electrodes in the cell in the same way you did in the petri
dish. If you found the potential to vary with depth, choose an appropriate depth and stick to it.
10. Record any decisions or observations you made in your lab notebook.
3.3.5
Analysis
Examine the two equipotential plots you have created. Pay attention to the lines of symmetry in each plot.
Mentally draw a straight line through the axis of symmetry of each plot.
Q8. Describe the shape of each equipotential plot, including the lines of symmetry, if any.
Q9. What differences do you notice?
For each electrode configuration, use Excel to create a plot of potential versus position along the axis of
symmetry, starting from the ground (0 V) electrode. Include the potential you measured at each electrode.
Q10. Use your laptop’s snipping tool to snip and paste an image of each plot here. Each plot should have
a title and axis labels.
Q11. In SI base units, a newton (N) is kg·m/s2 and a coulomb (C) is A·s. Use dimensional analysis to
write the units of the electric field in terms of volts (V = (kg·m2)/(A·s3)). 11
Q12. Use your plot to help you calculate the force in Newtons experienced by a 1 coulomb test charge:
a. 1 cm from the positive electrode (consider only the region between electrodes)
b. Equidistant from both electrodes
c. 1 cm from the negative electrode (consider only the side between electrodes)
For each plot, draw arrows to indicate the electric field lines.
Q13. How are the two electrode configurations different? Describe the characteristics that distinguish the
electric fields created by the two configurations.
Q14. Is there a region in either configuration where the potential change is close to linear? Where?
Q15. What is the purpose of the electrolyte in this experiment?
Q16. What effect, if any, does the shape of the electrolyte container have on the shape of the electric
field?
3.4
POST-LAB ASSIGNMENT
Be prepared to share your answers to these questions with the class.
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Consider the geometry of electric field in the gel electrophoresis cell. In the next experiment you will put
an agarose gel on the platform in the middle of a cell like this.
Q17. Why is the electrode in the electrophoresis cell shaped the way it is?
Q18. What will happen to charged molecules when they are placed in this electric field?
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