AZT-MI1 - Magnetic induction

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Iowa State University *

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3210L

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Physics

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Apr 3, 2024

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15

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Lab MI1 – Page 1 Lab MI1 - Magnetic induction Equipment USB digital oscilloscope (PicoScope 2204A), with two probes Picoscope Quick Guide (there should be a hard copy of this document on each table, and it is also posted as a PDF in this experiment’s module on Canvas.) 4 banana wire plugs with loops Function generator 1 BNC to double lab wire adapter Magnet bar 3200-turn coil Solenoid Mounted coil with adjustable number of turns and adjustable orientation. 300- resistor Goniometer Assortment of lab wires
Lab MI1 – Page 2 Preparation of the oscilloscope Turn all instruments off and remove all wires and cables from the terminals of the instruments. Open the PicoScope 6 software (on your computer’s desktop). Connect the BNC end of one probe to channel A of the oscilloscope. The pointy end of the probe can be pulled back to reveal a hook. Snap the probe hook and the probe ground to two of the banana plugs with loops. Make sure the attenuation switch on the side of the probes is set to X1. Probe compensation Before we proceed to more precise work, we need to check the compensation of the two probes on your table. The instructions to check and correct the compensation of a probe are on the second page of the PicoScope Quick Guide. Have you checked the compensation of both probes? yes Once the compensation is completed, move the attenuation switch on the sides of the probes back to X1. Done? yes
Lab MI1 – Page 3 Activity 1: Coil and magnet For this activity, we will use the small 3200-turn coil shown on the right, and the small bar magnet. Connect the channel A probe to the ends of this coil. Oscilloscope settings: Trigger: Auto on channel A (keep this for the entire lab). Channel A: 5 V, 1 s/div (adjust as needed, this is just a good initial setting) Orient the coil with the label that indicates the number of coils toward you (the label will be upside down). Move and hold the magnet in various ways through or near the coil, until you become familiar with what actions or arrangements result in an induced EMF detected by the oscilloscope. 1.1. Can you find any location of the magnet with respect to the coil at which the magnet generates an EMF in the coil when both the coil and magnet are at rest? Explain. 1.2. Thrust the magnet into the front face of the coil south pole first (positions 1 to 2 in the figure), and then pull it out.
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When you look at the graph you can see that when the magnet is going into the coil, it increases but when the magnet comes out of the coil, volatge decreases. Lab MI1 – Page 4 Insert below a scope display showing this EMF. Indicate on the figure the parts that correspond to the magnet moving in and out of the coil. Explain how the signs of the observed EMF in both parts is consistent with Faraday’s law. How does the speed of the motion of the magnet affect the observed EMF? Is this result consistent with Faraday's law? Explain.
When inserting the north pole first we can see that the voltage decreases once the magnet in the coil and then it decreases when the magnet comes out of the coil. Lab MI1 – Page 5 1.3. Now thrust the magnet into the front face of the coil north pole first, and pull it out. Discuss the differences with having the south pole first.
Lab MI1 – Page 6 ε ε Activity 2: Time-dependent magnetic field produced by a solenoid Background Consider a coil with N turns, each with cross-sectional area A , in a uniform magnetic field B , as shown in the figure to the right. The area vector of the coil A makes an angle θ with the direction of the magnetic field. The magnetic flux through the coil is given by: B NB A NBA cos θ If this flux changes with time, an EMF will be induced in the coil. According to Faraday’s law, the magnitude of this induced EMF is determined by the rate of change of the magnetic flux: induced  B t In today’s setup, the reason the EMF changes is that the magnitude of the magnetic field depends on time. Then, induced N B A cos θ t
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Lab MI1 – Page 7 Experimental setup The apparatus for the rest of the lab consists of two circuits, each connected to one channel of the oscilloscope. The exciter circuit It consists of the function generator, the solenoid and the resistor. Channel A of the oscilloscope is used in this setup to measure the voltage across the resistor. Note that the probe is connected to a circuit that has a defined ground –the black terminal of the function generator. Therefore, things must be wired in such a way that this ground is connected to the oscilloscope’s ground. The test circuit Connect the probe to the black and blue terminals. In this position, the probe is connected to a test coil
Lab MI1 – Page 8 with 400 turns. (Other combinations produce a coil with N = 100, 200 and 300 turns. Feel free to play with them a bit, but we will not use them formally in the lab). The case with the coil is hinged, so the orientation of the coil inside the solenoid can be adjusted. For now, keep the plane of the coil perpendicular to the bar. The voltage in the test coil will be detected by channel B in the scope. Keep channel B off until you are instructed to turn it on. Putting both circuits together Insert the coil inside the solenoid. Be careful: if the test circuit does not slide easily into the solenoid, do not force it! In particular, make sure you do not pinch the wires between the support of the test coil and the solenoid. Qualitative understanding of the setup The magnetic field inside the solenoid is proportional to the current in the exciter circuit: B I . On the other hand, Ohm’s law at the resistor dictates that the current must be proportional to the voltage across the resistor. Therefore, B V R , so the time dependence of the magnetic field in the solenoid is the same as the time dependence on channel A. Let us explore this qualitatively for several signals. a. The triangle function Oscilloscope settings: Trigger: Auto on channel A (keep this for the entire lab). Channel A: 10 V, 1 ms/div (adjust as needed, this is just a good initial setting). Channel B off.
Lab MI1 – Page 9 Function generator settings: Triangle function. Frequency: 200-500 Hz (the exact value is not important). Maximum output level (keep this for the entire lab). Make sure that all four buttons in the middle of the front panel are OUT (keep this for the entire lab). The signal on channel A should be something like the first graph below. Draw how you expect each of the other three quantities to depend on time. Note that this is all about the exciter circuit. The test circuit might just as well be in another room for now.
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Lab MI1 – Page 10 Now imagine that the coil is finally inserted inside the solenoid, so induction can take place. Sketch the time dependence that you expect to obtain for the induced EMF in the test coil. Test it! You may finally turn on channel B. Insert below the scope display. Discuss any differences with your prediction.
Lab MI1 – Page 11
Lab MI1 – Page 12 Dependence on the orientation of the coil inside the solenoid The coil is hinged, so we can change its orientation. The figure to the right shows how to use the goniometer to measure the angle ϕ between the plane of the coil and the axis of the solenoid. Note that the axis of the hinge of the goniometer must be aligned with the axis of the hinge of the coil case! Be very gentle when you handle the coil. Do not put tension on the wires and do not touch the soldered connections! Data collection The oscilloscope has a tool to measure the amplitude of a signal: open the “Measurements” menu, select “Add Measurement”. Then, choose Peak-to-Peak for channel B, measured on the Whole trace. The Peak-to-Peak value is in fact twice the amplitude, but you should record the Peak-to-Peak value, the “raw data”, and do any manipulation after that, during the Data Analysis. Measure and record on a table the Peak-to Peak value of the induced EMF in the coil for 10 different values of ϕ between 0 and 90 (including these two values). Insert your table below.
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Lab MI1 – Page 13
Lab MI1 – Page 14 Data analysis In the Background section, we obtained that the magnitude of the EMF should depend on the orientation of the coil as: ε induced cos θ where θ is the angle between the magnetic field and the area vector of the coil. Your goal is to verify if the collected data fits this theoretical prediction. Tips: In the lab, you measured angle ϕ , not θ . The goal is to verify the proportionality, but we will not bother with the proportionality constant. Therefore, the error discussion should be limited to the regression coefficient. Show all your calculations and graphs. Insert a snapshot of your table showing any extra columns you may have added.
Lab MI1 – Page 15 Conclusion Does your data fit the theoretical prediction? You must justify your answer based on your data.
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