SP212 Lab: Eight à Faraday’s Law and Inductance
Version: March 27, 2015
Physics II
Lab 8
SP212
Note: In today’s lab exercise, we will need to use sampling rates of 200 to 500 samples per second in Logger Pro. At data rates this high, you may notice that
Logger pro seems a bit slow; this is normal.
I.
Procedure
A.
Preliminary Training
CAUTION: Please try to keep the magnets from falling on a hard surface or coming into contact with another magnet. Both processes can destroy a good magnet.
1.
First, practice using Lenz’s Law with a bar magnet and a coil: You need to be able to use Lenz’s law to determine the direction if the induced E mf in order to complete today’s exercise.
Do the following experiment to make sure you can use Lenz’s law effectively. i.
Examine your 3200-turn coil, and note the direction in which the coil is wound. (It is marked on the coil.) Place your coil on the table with the label showing the number of turns facing up.
Connect the positive voltage clip to the bottom terminal of the coil, and the negative voltage clip to the coil’s top terminal. Now, for this configuration, predict the sign of the voltage that will be induced if you:
1.
Move the North end of your bar magnet toward the coil.
2.
Move the North end of your magnet away from the coil.
3.
Move the South end of your bar magnet toward the coil.
4.
Move the South end of your magnet away from the coil.
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SP212 Lab: Eight à Faraday’s Law and Inductance
Version: March 27, 2015 ii.
Follow the three steps to set Logger Pro up to take data with the voltage sensor: Experiment -> Set Up Sensors, Experiment -> Data
Collection -> length = 4 s, Experiment -> Data Collection -> Sampling
Rate = 200 samples/sec. Now, take data to test the four predictions you just made. How did you do?
2.
Once you are satisfied that you can use Lenz’s law effectively, you may go on. There is nothing to turn in for this part of the exercise.
B.
Taking Data: Faraday’s Law
1.
Now we are ready to take data. This is easiest if you follow these steps:
BE CAREFUL: If you drop a magnet onto a hard surface, you can ruin the magnet. i.
Designate one lab partner as magnet dropper and catcher, and the other lab partner as coil and tube holder.
ii.
Place the plastic tube in the coil as your instructor demonstrated. iii.
Zero the voltage probe, and measure the E mf induced in the coil as the magnet slides down the tube and through the coil, first, North pole leading, then, on a second drop, South pole leading. My own data is attached as a sample… but I only did one drop. iv.
Use Analyze -> Integral to measure the area under the curve for each magnet drop: First, measure the area under the entire voltage pulse. Gauss’s Law for the Magnetic Field implies that this integral should be zero. We’d like to test this, but Logger Pro does not help us estimate the uncertainty in the integral. Therefore, measure the areas under the positive and negative lobes separately. Treat the areas of both lobes as positive, and find the ratio of the difference to the average , and express the ratio as a percentage.
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SP212 Lab: Eight à Faraday’s Law and Inductance
Version: March 27, 2015
2.
Discussion: In a few complete sentences organized into a short paragraph, discuss how Gauss’s Law for the Magnetic Field implies that the area under an entire pulse should be zero. Then, discuss whether your data supports or fails to support Gauss’s Law for the
Magnetic Field.
C.
Two Coils Linked by a Soft Iron Yoke
1.
SETUP: i.
Place the two 3200-turn coils side-by-side on the table, oriented in the same direction. ii.
Link the coils, in the magnetic sense, with the soft iron yoke, as your instructor demonstrates. iii.
Connect the digital function generator (DFG) to the coil on the left; this will be the primary coil. Use the black and red terminals on your DFG. Make sure you connect these terminals, and the two voltage sensors, observing the polarities your instructor diagrams on the blackboard. iv.
The voltage sensors measure the voltages across the primary and secondary coils. Since the primary is the “cause,” and the secondary is the “effect,” it is easy to compare if we all agree to place the graph for the primary below that for the secondary on the page in Logger Pro. With this setup, let’s do four experiments, changing one thing at a time.
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SP212 Lab: Eight à Faraday’s Law and Inductance
Version: March 27, 2015
2.
Primary Voltage: Triangle Wave, Frequency = 1 Hz,
Amplitude = 5 V. i.
Zero both voltage sensors, adjust the DFG output as suggested, and take 5 seconds worth of data, recording the primary and secondary voltages. ii.
ANNOTATE: Put proper labels on the graphical axes, give the graph an experiment number, and a title, and so forth. Note the amplitude and frequency of the secondary voltage.
3.
Primary Voltage: Triangle Wave, Frequency = 2 Hz,
Amplitude = 5 V. i.
Adjust the primary voltage as suggested, take 5 seconds worth of data, and annotate. ii.
Discussion: What happens to the secondary voltage when you double the primary frequency , but leave the primary voltage unchanged? Why?
4.
Primary Voltage: Sine Wave, Frequency = 2 Hz, Amplitude
= 5 V. i.
Adjust the Primary voltage, take 5 sec worth of data, annotate. ii.
Discussion: What is the effect of switching from triangle input to sine wave? Why?
5.
Primary Voltage: Sine Wave, Frequency = 2 Hz, Amplitude
= 5 V, but remove the iron core. i.
Remove the core, take 5 sec of data, annotate, and… ii.
Discuss what happened and why we like soft iron yokes.
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SP212 Lab: Eight à Faraday’s Law and Inductance
Version: March 27, 2015
D.
Measuring the Self-Inductance of a Coil with a DMM.
1.
200-turn Field Coil. i.
First, measure the radius of the coil and predict the inductance of the coil. ii.
Then, measure the inductance with the Mastech. You’ll have to look up the appropriate uncertainty codes. iii.
Do they agree with each other and with your calculation?
Answer in your discussion.
2.
3200-turn Field Coil. i.
This is not a flat coil, nor is it a solenoid. But its inductance should be between the inductance of a flat coil with the same number of turns and same average diameter, and that of a similarly-dimensioned solenoid.
Calculate both inductances. ii.
Then, measure the inductance with the Mastech. You’ll have to look up the appropriate uncertainty codes. iii.
Discuss whether or not your measurements agree with each other, and with your calculated values.
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SP212 Lab: Eight à Faraday’s Law and Inductance
Version: March 27, 2015
E.
Quantitative Test of Faraday’s Law:
1.
Preliminary Data: The primary coil has 200 turns, and its radius is written on the coil. The secondary has 3200 turns; you’ll have to measure its length.
2.
Use your 200-turn coil as the primary, and connect the black and red terminals of the DFG to the terminals on the 200-turn coil, and connect a current sensor to measure the current in the primary coil.
3.
Place the 3200-turn coil at the center of the primary coil, and connect the secondary voltage sensor.
4.
Set the DFG for a 5 Hz, 0.5 V triangle wave, and take 2 seconds worth of data.
5.
Use Analyze -> Slope to find the derivative of the current in the primary, and Analyze -> Statistics to find the mean value of the emf that’s induced in the secondary.
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SP212 Lab: Eight à Faraday’s Law and Inductance
Version: March 27, 2015
F.
1.
Annotated and labeled graph from Part B, with discussion.
2.
Four graphs from Part C, with discussions.
3.
Graph from part D, with calculations and discussion.
4.
Calculation and measurements from part E.
Don’t forget uncertainties, units, annotations and discussions.
II.
Clean-Up
A.
Golden Rule: “Do unto others as you desire them to do unto you.”
This applies as much here in the lab as it does in the Fleet. As future Naval Officers, how can you expect your enlisted sailors to maintain a clean work area if your stateroom, work areas, mess area, etc is a “pig sty?” So as officers it is imperative that we clean up after ourselves not only to follow the Golden Rule, but also to lead by example for the enlisted personnel under our charge.
1.
End of Lab Checkout: Before leaving the laboratory, please tidy up the equipment at the workstation and quit all running software.
2.
The lab station should be in better condition than when you arrived and more importantly, should be of an appearance that you would be PROUD to show to your legal guardians during a “Parents Weekend.”
3.
Have your instructor inspect your lab station and receive their permission to leave the Lab Room.
4.
You SHALL follow this procedure during every lab for SP212!
Many thanks to Dr. Huddle and Dr. Fontanella for their assistance in producing this Laboratory procedure; specific references can be supplied on request. LCDR Timothy Shivok
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