FIELDS III.
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INTRODUCTION This experiment is a continuation of studies on electrostatic elds discussed in the previous experiment.
PURPOSE In the previous experiment we traced equipotential lines for various electrostatic elds. The equipotential lines provide useful qualitative description of such elds. In this experiment we will study electrostatic elds in a quantitative way. The measurement process will be computerized.
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PRE-LAB ASSIGNMENTS A. Readings: Electric potential and electric eld vector were discussed in the theoretical introduction to the previous experiment. You may need to read it again. Additional formulae are given below. Electric eld E between two parallel plates, separated by distance d and kept at the voltage dierence V , is uniform (i.e. it has a constant magnitude and direction). It is directed from the positive electrode to the negative one. The value of the electric eld strength is given by: V E= d The potential in between the plates is changing linearly as a function of the distance from the negative plate (x): V = V0 + E x . The electric eld due to concentric cylinder(s) is E= 2 0 r
where has to do with the cylinder charge and r is the distance to the center of the cylinders. This formula implies logarithmic dependence of V on r: V = V0 + ln(r) (where is a constant related to ). B. Exercises: Please answer the questions on Report Sheet III1, which will be collected at the beginning of the laboratory session and graded by your instructor.
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REPORT SHEET III1 Date Instructor PRE-LAB EXERCISES Exercise 1. How would the electric eld strength between the two parallel plates change if you doubled the distance between the plates kept at the constant potential dierence? Name
Exercise 2. What is the direction of the electric eld vector in between the two parallel plates with some potential dierence.
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LABORATORY ASSIGNMENTS
Computer interface box
Tray + Battery Water
DIN1 PORT2
Electrode
DIN1
Electrode
Probe #1
Probe Wooden guiding block Cart
Amplifier
Motion Detector
Figure 1. Diagram of the experimental set-up for measuring potential as a function of position in between the electrodes.
Experiment AF: Quantitative Study Of Electrical Fields With The Electrolytic Tank Method
Materials Needed: Tray with tap water Electrodes: (A-D) Two at plates, (E-F) 1 inch (or 1/2 inch) and 8 inch cylinders. Battery (4.5 V) Probe mounted on a cart Wooden guiding block Dual Channel Amplier with voltage probes ULI computer interface box Voltmeter ELECTROSTATIC FIELDS (CONTINUATION) III-5
Cables (B-F) Motion Detector The Task: To graph potential and electric eld strength as a function of the probe position. Procedures A-1. The electrical circuit in this experiment (see Fig. 1) is essentially the same as in the previous one, except that instead of the power supply, we will use a 4.5 V battery to generate a potential dierence between the electrodes, and instead of the hand-held digital voltmeter, we will use a voltage probe which is readout by a computer. Voltage probes should be connected to the Dual Channel Amplier (only the Probe 1 will be used in this experiment). The DIN1 output from the Dual Channel Amplier should be plugged into the DIN1 input on the ULI computer interface box. Make sure the ULI interface box is on (the ON/OFF switch is on the back panel of the box, there is a green power indicator light on the front panel). Start the computer, and click on the PHY222 icon to start the program which works with the voltage probe. If you happen to exit the program (which you should do at the end of the laboratory session) please do not save any settings to a le when the program oers you this option. To load the proper initialization le, choose Open. . . from the File menu. Open the le electriceld in PHY222 subdirectory. The voltage probe reading is shown near the bottom of the screen, in the small box which says Potential=. A-2. Check the voltage probe reading. Connect the red and black voltage probe leads to each other. The reading on the computer should be close to zero. Measure voltage supplied by the battery with the hand-held voltmeter (if it is below 1V, the battery is dead and you need a new one). Then connect the computer voltage probe to the battery and see if you get similar reading with the computer. If the voltage probe is o by more than 0.3V at any of these two voltage readings, the probe is not working properly (ask the lab instructor for help). A-3. If the probe passed the test described in the previous step, but its readings disagree with the voltmeter measurements by more than 0.1V, you can improve its accuracy by changing its calibration. To calibrate the voltage probe go to Calibrate under the Experiment menu. Click on DIN1 and then on Perform now button. With the voltage leads connected to each other, enter 0 in the Value 1 box and then click on the Keep button. Now connect the voltage probe to the battery (the black lead to to the black connector, red to red) and enter in the Value 2 box whatever value you measured with the hand-held voltmeter. Click on Keep and then on the OK button. Check how well the probe measures zero volts and the battery voltage again (see the previous step). If you get weird readings, try calibrating again and if it doesnt help, the probe may be broken (ask for help). III-6 ELECTROSTATIC FIELDS (CONTINUATION)
A-4. Set up the electrical circuit as shown in Fig. 1. The tray should be clean, without residue on the bottom. Use fresh, clean tap water. Use two at plate electrodes, separated by 14cm (electrodes at the 7cm mark) along the longer dimension of the tray with tap water. The red lead of the voltage probe should be connected to the probe mounted on the cart. The black lead should be connected to the negative pole of the battery also indicated by the black color (you can clamp the lead on the electrode connected to that pole). Use a wooden board to guide the probe along the middle line of the tray. Make sure that at any position of the cart the probe tip is well under water and that it is not getting stuck on the bottom of the tray. A-5. Now we are ready to measure potential as a function of the position in between the electrodes. Record value of the potential readout from the computer for the probe positioned at 6cm, 5cm, 4cm, . . . , +6cm in the Report Sheet III2 (we use the minus sign to indicate positions closer to the negative electrode). Transfer these measurements onto the Potential vs. Distance graph on the same Report Sheet. You will need to set-up a range of the vertical axis by yourself. Make zero the minimal value on the graph. Choose a round number, higher than any of your measurements and easily divisible by 10 for the maximal value (e.g. 2V, 4V, etc.). Label some of the lines dividing the vertical axis to make graphing easier. Represent each measurement as a point on your graph. Draw lines connecting the neighboring points. A-6. The strength of the electric eld E along the scanned direction can be calculated from the formula: E = dV . Here dV is a dierence between values of the potential when dx the position of the probe is changed by innitely small amount dx. This formula is still approximately correct when a nite position change is taken. Thus, we will set dVi = Vi Vi1 where i is the index numbering your voltage measurements. Since we i changed the probe position in 1cm steps dxi = xi xi1 = 0.01m, and Ei = dVi = dx dVi 100 V/m. Calculate the dVi column in the Report Sheet III2 and transfer these results onto the Electric Field Strength vs. Distance graph. Again, you will need to set up a range of the vertical axis by yourself. Make zero the maximal (or the minimal) value on the axis. Answer the question at the bottom of the Report Sheet.
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REPORT SHEET III2 Date Instructor A. i 1 2 3 4 5 6 7 8 9 10 11 12 13 xi 6 5 4 3 2 1 0 1 2 3 4 5 6
6 5 4 3 2 1 0
V Ei ( m )
Name Partner(s) Potential vs. Distance
Vi
Vi Vi1 Vi (V)
6 5 4 3 2 1 0
Probe Position xi (cm)
1
2
3
4
5
6
Electric Field vs. Distance
Probe Position xi (cm)
1
2
3
4
5
6
Are your measurements of the potential vs. distance and of the electric eld strength vs. distance roughly consistent with the theoretical expectations? Explain.
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B.
You may wonder why you have been asked to use the computerized voltage readout instead of hand-held voltmeter to perform the experiment A. We will repeat the previous experiment with fully automated voltage and probe position measurements. This will be a good illustration of the benet of computerized experiments. The probe position will be located with the Motion Detector connected to PORT2 of the ULI interface box. The red light on the Motion Detector should be on. Position the Motion Detector at the end of the wooden board facing the cart. The closest position of the cart to the Motion Detector should be at least 0.5m (the Motion Detector will fail for smaller distances). Make sure that there are no obstacles between the Motion Detector and the cart (like wires or parts of your body). Do not hold the cart by the end facing the Motion Detector. To start collecting data click on Collect button above the computer graphs. The data will be collected for ten seconds. The two graphs on the left will show how the readout from the Motion Detector (the top graph) and from the voltage probe (the bottom graph) is changing with time. Of course, we are not interested in time dependence but in the dependence of the potential and electric eld strength on the probe position which are shown by the two graphs on the right. The electric eld strength is calculated by the from computer the voltage measurement by numerical dierentiation similarly to the calculation you did manually in the experiment A (except that the dxi intervals are now much smaller since the computer collects 20 measurements per second). For the electric eld measurement it is important that you move the probe from one electrode to the other relatively fast imagine what happens when the probe is not moving at all: dxi and dVi are both zero and our measurement of E is 0/0 which has an undened value (for that reason some entries in the computer graph of E should be ignored). Move the probe from one electrode to the other in one stroke and then stop (leaving the rest of the time unused) or move the probe back-and-fourth between the electrodes until the time runs out. Experiment with dierent probe motions until you are satised with the results. Copy what you see on the screen to the Report Sheet III3. It is not important that you copy the computer graphs with great precision. Just try to reproduce the most important features. Indicate range of values on the horizontal and vertical axes (e.g. copy to your report the position of the lowest and the highest number describing the axis on the computer graph). Notice that the horizontal and vertical lines on the computer graphs and on the report sheet graphs have a dierent pattern. Nevertheless they should be helpful in tracing the data curves. Compare the results you have obtained here with the results obtained in the experiment A. Are they in qualitative agreement?
C.
In this experiment we will try to verify the theory for the dependence of the electric eld strength on the separation of the two at electrodes. Read out the value of the electric eld in the middle point between the two electrodes from the data you collected in point B. You can do it by eye from the graph, or you can make the computer help you by clicking on Examine in the Analyze menu. Now position the pointer at III-11
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the point of the Distance vs. Time graph which corresponds to the middle point. The computer will display the corresponding value of the other displayed variables for this point. Record this electric eld strength at the bottom of the Report Sheet III3. Now double the electrode separation (position them at 14cm). Collect the data for this new conguration and determine the electric eld strength in the middle point. Record the measured value in the Report Sheet III3 and answer the question.
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REPORT SHEET III3 Date B. Instructor Distance vs. Time Name Partner(s) Potential vs. Distance
x (m)
V (V)
0
1
2
3
4
Time (s)
5
6
7
8
9
10
Distance (m) Electric Field vs. Distance
Potential vs. Time
V (V)
dV dx
V (m)
0
1
2
3
4
Time (s)
5
6
7
8
9
10
Distance (m)
C. Value of the electric eld strength in the midpoint between the electrodes for the data shown above E = for the twice larger plate separation E = Does the change of electric eld strength with doubling the plate separation roughly ELECTROSTATIC FIELDS (CONTINUATION) III-13
agree with the theoretical expectations? Explain.
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D.
So far we have been moving the probe from one electrode to the other. This determines the value of electric eld in the direction perpendicular to the electrodes. The electric eld is a vector, thus in principle, it could have some value in the direction parallel to the plates. Reposition the electrodes at 7cm points along the short tray direction. The probe is still moving along the long tray dimension, which is now parallel to the electrodes. We will measure component of electric eld in this direction 1cm away from the positive or negative electrode (not in the middle between the electrodes!). You may need to reposition the tray with respect to the probe. Collect the data including the points beyond the extent of the electrodes. Copy what you see on the screen to the Report Sheet III4. Record the value of the electric eld near the center of the electrode at the bottom of the report sheet. Answer the questions.
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REPORT SHEET III4 Date Instructor Distance vs. Time Name Partner(s) Potential vs. Distance
D.
x (m)
V (V)
0
1
2
3
4
Time (s)
5
6
7
8
9
10
Distance (m) Electric Field vs. Distance
Potential vs. Time
V (V)
dV dx
V (m)
0
1
2
3
4
Time (s)
5
6
7
8
9
10
Distance (m)
Value of the electric eld strength near the plate center E = The theory says that in between the electrodes the electric eld vector should be directed from one electrode to the other. Therefore, the value measured here should be small compared to the electric eld in the perpendicular direction measured previously ELECTROSTATIC FIELDS (CONTINUATION) III-17
for the same separation of electrodes. Compare the value above with the result in the Report Sheet III3.
(see also the question on the back of this page) Try to relate what happens to the value of electric eld beyond the extent of the electrodes as compared to the value near the electrode center (observed in this experiment) to the pattern of equipotential lines you traced for this set-up a week ago.
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E.
In this experiment we will measure electric eld for the 1 inch (some set-ups use 1/2 inch) and 8 inch concentric cylinders. Put the center small cylinder on the positive potential. Congure the probe to pass near the inner cylinder as close as possible. Collect the data when you move the probe from one side of the outer cylinder to the other, passing near the inner cylinder in the middle (you can move back-and-forth). If the measured values of E go beyond the range displayed at the bottom right graph, you will need to change the graph range. To change the minimal (or maximal) displayed value click on it on the graph, and type in a new value. You can also click at any other point in ...