Physics 2 Lab 10

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Massachusetts Institute of Technology *

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Electrical Engineering

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Oct 30, 2023

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Faraday’s Law Lab Number and Title: 223 Faraday’s Law Name: Aaron Hsu Group ID: N/A Date of Experiment: 11/29/22 Date of Submission: 12/6/22 Course and Section Number: PHYS 121A013 Instructor’s Name: Matias Daniel de Almeida Partner’s Names: Paul Svorec, Alex Ack, and Noah Francois 1. Introduction: The goals and objectives of this lab are to show and display Faraday's law of electromagnetic induction. Familiarize and understand the concepts of changing magnetic flux and induced current associated with Faraday’s law of induction. Faraday’s law of induction states that a changing magnetic flux through a coil generates an emf in the wire. This is called electromagnetic induction which explains that if you move a bar magnet through a loop of wire you will create electricity through the wire. When pushing the bar magnet into the loop of wire then the magnetic flux through the wire increases because the magnetic field strength in the cross sectional area of the coil increases. Then when you pull the magnet back out of the coil then the magnetic flux through the coil decreases. Instead of using a bar magnet we use a helmholtz coil instead in order to fluctuate magnetic flux through the induced coil. The magnetic field strength that is produced by a coil increases as the current in the coil increases and helmholtz coils produce a uniform magnetic field between the two coils. The helmholtz coils are connected to a power source that electrical current in the helmholtz coils can linearly increase or decrease over time and hence magnetic field strength between them will linearly increase or decrease over time. This means that there will be a constant change either negative or positive in magnetic flux through the small coil which then induces emf. The voltage induced in a coil by a changing magnetic field B(t) through the coil is measured and compared with the predictions of Faraday’s law. Magnetic flux Φ ? through a loop of wire is When the magnetic flux through the loop of Φ ? = ∫ ? · 𝑑?.

wire is changing over time, the loop opposes the changes by inducing emf which is . The negative sign in this equation shows that the induced emf and the ε =− 𝑑Φ ? 𝑑𝑡 change in magnetic flux will have opposite signs. This means that if the magnetic flux from the helmholtz coils increases over time through the small coil, then the induced current in the small coil will have a direction in order to reduce the amount of magnetic flux change through it. If the loop of wire made of N turns and cross-section area A is aligned normally with uniform magnetic field B then the equation is . ε =− 𝑁?( 𝑑? 𝑑𝑡 ) The magnetic field strength created by the helmholtz coils can be theoretically calculated from . is the number of turns of helmholtz coil, R is the radius, and ? = 8.992×10 −7 𝑁 ℎ 𝐼 𝑅 𝑁 ℎ I is the current. Then since the magnetic field strength is linearly proportional to the current, the equation then turns into . When the ?(𝑡) = 8. 992 × 10 −7 ( 𝑁 ℎ 𝑅 )𝐼(𝑡) helmholtz coils are connected to the signal generator we will make the current through the coils linearly changing over time which then means the change in magnetic field strength over time is linearly proportional to the change in current over time which gives us the equation . Then from combining the two 𝑑?(𝑡) 𝑑𝑡 = 8. 992 × 10 −7 ( 𝑁 ℎ 𝑅 ) 𝑑𝐼(𝑡) 𝑑𝑡 equations we get . When all of these parameters ε =− 8. 992 × 10 −7 (𝑁?)( 𝑁 ℎ 𝑅 ) 𝑑𝐼(𝑡) 𝑑𝑡 are fixed the emf induced in the small coil will be linearly proportional to the change in current through the helmholtz coils and the sign of emf is opposite to that of change in current. 2. Experimental Procedure: The equipment that we used for this lab are a voltage sensor, coil base, banana cables both red and black, small coil (2000 turns, 2.3 cm inner diameter, 3.8 cm outer diameter), lab computer with capstone software installed, two coils (500 turns, 10.06 cm inner radius, 11.37 cm outer radius, 1.6 cm width), 850 universal interface, ruler, magnetic field sensor, right angle clamps, compass, 2 stands with a rod, and a high current sensor. We followed the same procedure as stated in the lab manual except we also had to change the angle to 45 degrees and record our results for the 45 degree angle. Before getting into the procedure of the experiment we first had to make sure that the setup was correct and

right. We had to make sure that all of the banana cables were connected in the right spots and set up the two helmholtz coils to be a certain distance away from one another to be the radius. We then would make sure that the interface and the current sensor are connected correctly with each other and the coils with the banana cables. We then would set up the small coil so it is in the middle between the two helmholtz coils by using the rod and the angle clamps to hold it up and then connect it correctly with the voltage sensor. We finally would set up the magnetic field sensor by using another rod and an angle clamp to hold it up and connect to the interface and have it faced towards the two helmholtz coils and the small coil. We first would record our data for our coils with the radius, turns, cross sectional area, and the number of turns. We then would set up the lab computer by going to the right folder for the experiment and then in the measurement page we would set the frequency to 2 Hz, amplitude to 5 V, and voltage offset set to 5 V. We then will linearly increase and decrease the current through the helmholtz coils over a certain period of time and hence the magnetic field strength between the coils will linearly increase and decrease. Before running and recording the experiment we need to make sure to tare the magnetic field sensor and then click record on the lab computer. We then would analyze the graphs after recording by using the lab computer to find the slope and use the equations for our calculations. We then would repeat this for setting the frequency to 4 Hz as well as repeating this for positioning the small coil to an angle of 45 degrees. 3. Results: 2hz data:

Physics 2 Lab 10

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