Lab8_VanLe

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Jan 9, 2024

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Van Thin Le Professor Xiang Song Phys-2426-51700 25 October 2023 Lab 8: Faraday’s Electromagnetic Lab Part A Theory Please study induction concept to answer the following questions. 1. Discuss magnetic flux and list its equation. Explain Faraday’s law and list its equation. Magnetic Flux: Magnetic flux (Φ) measures the magnetic field passing through a surface and is defined as Φ = B ⋅ A ⋅ cos(θ), where B is the magnetic field strength, A is the surface area, and θ is the angle between the field and the surfaces normal. Faraday's Law: Faraday's law of electromagnetic induction states that the induced electromotive force (emf) in a closed circuit is equal to the negative rate of change of magnetic flux through the circuit, expressed as ε = dϕ dt . It signifies how a changing magnetic field induces a voltage in a conductor, and the negative sign denotes the direction of the induced current, which opposes the change in flux. 2. Discuss Lenz’s law. Apply Lenz’s law to find the directions of induced current for Figure (a) and (b). Which side crossing R (left side of R or right side of R) has higher voltage for case (a) and case (b)? Lenz’s Law states that the induced current in a loop is generated in a direction that produces a magnetic field opposing the change in magnetic flux within the loop's enclosed area. This opposition is represented by the negative sign in Faraday's law.

In (a), when a north pole approaches the coil, the coil responds by creating a virtual north pole to counteract the approaching magnet. This action induces a counterclockwise current concerning the bar magnet. In scenario (b), the coil generates a virtual north pole on the side facing the magnet to attract it when the north pole is moving away. This results in the induction of a clockwise current concerning the bar magnet. In (a), the south pole exhibits a higher voltage when it crosses point R, and in (b), the north pole exhibits a higher voltage when it crosses point R. 3. A circular coil consists of 3 turns of wire with radius r = 3.5 cm. A uniform magnetic field directed perpendicular to the plane of the coil is shown in the figure. From t = 0 to t = 0.032 s, the field changes from 0.0012 to 0.023 T. What is the induced emf during this time interval? e =− NA dB dt ¿ − Nπ r 2 dB dt ¿ − 3 ×π× 0.035 2 × 0.023 − 0.0012 0.032 − 0 ¿ − 7.87 × 10 − 3 V 4. In question 3, if the resistance R = 12 Ω, what is the induced current in this time interval? What is the direction of induced current? Which position has higher voltage V A or V B ? V = IR →I = V R ¿ − 7.87 × 10 − 3 12 = 6.55 × 10 − 4 The current's direction, determined by the right-hand rule, is to the right, signifying a clockwise motion (→). VB exhibits a higher voltage than VA.

Part B Lab Go to PhET website. Click on Simulation/Physics. Under Physics, choose Electricity, Magnets & Circuits. Under Electricity, Magnets & Circuits, Faraday’s Electromagnetic Lab is the 15th simulation (Location might change. A to Z search.). Click to run the Faraday’s Electromagnetic Lab . I. Complete Data Table with Pickup Coil Simulation: Basic Operation for Pickup Coil Simulation: Click Pickup Coil tag on the top. Set the Strength scale to 100% (default 75%). Place check mark on Show Field. Click on the Voltmeter as indicator. Change the Loop turns into N = 1 turn. Keep the Loop area 50% as default. Hold and drag the magnet moving forward and backward completely through the center of coil as fast as you can till you observe the maximum induced voltage, V max , and record in Table. Change the Loop turns into N = 2 turns and repeat the process to complete Data Table 1. Data Table 1: Measure Maximum Induced Voltage Assume the voltmeter (V) scaled as showed in the Figure. Assume the radius of coil r = 3 cm = 0.03 m and area A = π•r 2 . Calculate the time rate change of magnetic field dB/dt = V max /(N•A). Attach a screenshot of N = 1 turn Data from the Simulation to lab report . N (# of loops) V max (V) dB/dt (T/s) 1 1.9 672 2 3.7 654 3 5 589

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Questions: • Give physical explanation what causing induced emf (voltage) in this experiment. When a bar magnet is moved into or out of a coil, it induces an electromotive force (emf). The direction of motion dictates the emf's sign, with reversed poles yielding opposite signs. This principle applies whether it's the magnet or the coil in motion; what matters is their relative movement. Faster motion generates a stronger emf, and no emf is induced when the magnet is still relative to the coil. • Why does the needle of Voltmeter move left and right when the magnet moves back and forth through the coil? The approaching magnet's alteration of magnetic flux triggers a voltage in the loop, which is then measured by the voltmeter. • Repeat the experiment with a slower fashion. When the magnet moves from left toward coil on the right, which side crossing the resistor has higher voltage? When the magnet passes through the coil, which side crossing the resistor has higher voltage? When the magnet approaches the coil, the north pole exhibits a higher voltage as it crosses R, and as the magnet passes through the coil, both sides have equal voltage. II. Complete Data Table with Generator Simulation: Basic Operation for Generator Simulation: Click Generator tag on the top. Set the Strength scale to 100% (default 75%). Place check mark on Show Field. Click on the Voltmeter as indicator. Change the Loop turns into N = 3 turns. Keep the Loop area 50% as default. Hold and slide the switch above the faucet and adjust the angular speed ω = 20 RPM

(green indicator at the center of magnet). Click the play button (►) at the bottom to start generator. Record the maximum induced voltage, V max , in Table. Repeat the process for a different ω to complete Data Table 2. Note: It might be easier to find the V max using the Step Button located on the right side of ►. Data Table 2: Measure Maximum Induced Voltage as Function of ω Assume the voltmeter (V) scaled as showed in the Figure. Attach a screenshot of ω = 100 RPM Data from the Simulation to lab report . ω (RPM) 20 40 60 80 100 V max (V) 1 2 3 4 5

Questions: • What is your conclusion from Data Table 2? The maximum induced voltage rises with an increase in angular speed, indicating a direct proportionality between the two. • Describe the working principle of this generator. A copper coil, tightly wound around a metal core, functions as an armature. This armature is swiftly rotated between the poles of a magnet, and it is connected to a shaft driven by a mechanical energy source like a motor, which, in this case, is powered by a water turbine. As the coil spins, it intersects the magnetic field between the magnet's poles, leading to the induction of electric current as the magnetic field interacts with the electrons within the conductor. Part C Discovery Beyond what you have done with Pickup Coil and Generator , you can make more findings , or give real life examples for Induction. You can express your findings by data table, word, equations, and/or screenshot graph/Video, but do giving physics explanation. You could also design meaningful experiment and show it here. In Part C minimum 10 sentences are required. Electromagnetic induction finds diverse applications in everyday life. For instance, a magnetic flow meter, also known as a mag meter or electromagnetic flow meter, measures fluid flow by exploiting the voltage generated when a liquid passes through a magnetic field. This innovative device employs Faraday's law of electromagnetic induction. It necessitates a conductive fluid, such as ion-containing water, and an electrically insulating pipe surface, like rubber-lined steel. Similarly, transformers rely on electromagnetic induction to adjust voltage levels in electrical circuits, while electric guitar pickups convert string vibrations into electrical signals through induced voltage changes. Eddy current brakes in transportation systems utilize induction to slow down vehicles without physical contact, and security metal detectors employ it to identify concealed objects. In each case, changing magnetic fields induce currents or voltages in nearby conductors, showcasing the practical versatility of electromagnetic induction. Traditional magnetic flow meters face challenges when potential differences from electrochemical effects are indistinguishable from flow-induced differences due to a constant magnetic field. Modern designs tackle this by continually reversing the magnetic field, canceling out these potential differences, although this rules out the use of permanent magnets. Electromagnetic induction underpins the functioning of these technologies, making them indispensable in various fields and applications.

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