Electromagnetic Induction and Motional Emf PDF

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Practice problems on Electromagnetic Induction and Motional Emf...

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PHYS272 Problem Session: Induction: Faraday’s Law, Lenz’s Law, & Motional Emf C1. A conducting rod slides over two horizontal metal bars with a constant speed v to the right. The entire set up is in a region of uniform magnetic field that is perpendicular to the plane of the rod and bars. If the induced current through the resistor is as indicated, what is the direction of the magnetic field?

C2. The magnetic field through a circular loop of radius 15.7 cm varies with time as shown below. The field is perpendicular to the loop. Plot the magnitude of the induced emf in the loop as a function of time.

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C3. A wire of length L is wound around an iron cylinder mounted on a base. The two ends of the wire are connected to a battery via a switch that is initially open. A metal ring with a diameter larger than that of the cylinder sits on top of the coil. What happens to the metal ring when the switch is closed?

C4. A coil is moved from location 1 to location 5 through a magnetic field as shown in the diagram below. The field inside the rectangle is uniform and out of the page. The field outside the rectangle is zero.

What is the direction of the induced current in the coil when the coil is at each position (1,2,3,4,5) as it moves to the right?

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P1. A long straight wire carries a current of 5.90 A as shown in the figure. The distance r1 = 10.0 cm, r2 = 20.0 cm, and ℓ = 17.0 cm. Determine the magnitude of the magnetic flux through the area shown.

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P2. A long piece of wire is bent into a rectangular loop and placed on a table top in the horizontal plane. A very long straight piece of wire, placed as shown in the diagram below has a current I = a − bt2 flowing in the direction indicated. The wire is at a distance of d = 2.50 cm from the left side of the rectangular loop. What are the magnitude and direction of the induced emf in the loop at t = 1.28 s? Here a = 16.4 A, b = 1.56 A/s2, ℓ = 0.500 m, and w = 0.250 m.

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P3. A circular coil of 260 turns and radius 4.50 cm is placed inside and coaxial to a solenoid with 350 turns/m. If the current in the solenoid is represented by the equation I = a(1 − e−bt), where a = 14.5 A and b = 1.95 s−1, determine the magnitude of the induced emf in the coil when t = 1.50 s.

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