solutions_34 - PHY2061 R. D. Field Chapter 34 Solutions...

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PHY2061 R. D. Field Solutions Chapter 34 Page 1 of 6 Chapter 34 Solutions Problem 1: A long straight wire carries current I . Nearby and lying in the same plane is a circular loop, as shown in the Figure . If the loop is moved toward the wire, what will be the direction of the current induced in the loop (if any) and what will be the direction of any electromagnetic force exerted on the loop? Answer: counterclockwise; away from the wire Solution: Pushing the wire loop toward the current carrying wire causes the magnetic flux to increase in the loop and thus the induced current will flow in a counterclockwise direction so that the induced magnetic field will be up (opposite to the increasing downward external magnetic field). The force on the loop is in a direction that opposes the push (i.e. away from the straight wire ). Problem 2: A magnetic field given by B(t) = at+b with a = 1 T/s and b = -1 T is directed perpendicular to the plane of a circular coil of 10 turns and radius 0.2 m . If the coil’s total resistance is 1.58 Ohms , how much power ( in Watts ) is dissipated at time t = 1 s ? Answer: 1 Solution: The magnetic flux through the loop is Φ B = NB Α and from Faraday’s Law we have, NAa dt dB NA dt d B = = Φ = ε . At t = 1 second (actually at any time t) this gives R NAa R I = = , and power W s T R a A N R I P 1 58 . 1 ) / 1 ( ) 2 . 0 ( ) 100 ( 2 4 2 2 2 2 2 = = = = π . I
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PHY2061 R. D. Field Solutions Chapter 34 Page 2 of 6 Problem 3: A 25-turn coil of resistance 3 Ohms has area of 8 cm 2 . Its plane is perpendicular to a magnetic field given by B(t) = 0.4t - 0.3t 2 (where B is in Tesla and t is in seconds). What is the induced current in the coil ( in milliA ) at t = 1 second ? Answer: 1.33 Solution: The magnetic flux through the loop is Φ B = NB Α and from Faraday’s Law we have, ) 6 . 0 4 . 0 ( t NA dt dB NA dt d B = = Φ = ε .
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.

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solutions_34 - PHY2061 R. D. Field Chapter 34 Solutions...

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