E2HWCH28 - Chapter 28 Magnetic Induction 20 A uniform...

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Chapter 28 Magnetic Induction 20 A uniform magnetic field of magnitude 0.200 T is in the + x direction. A square coil that has 5.00-cm long sides has a single turn and makes an angle θ with the z axis, as shown in Figure 28-42. Find the magnetic flux through the coil when is ( a ) 0º, ( b ) 30º, ( c ) 60º, and ( d ) 90º. Picture the Problem Because the surface is a plane with area A and B is constant in magnitude and direction over the surface and makes an angle with the unit normal vector, we can use φ cos m BA = to find the magnetic flux through the coil. The magnetic flux through the coil is given by: cos m BA = Substitute for B and A to obtain: ( 29 ( 29 cos Wb 10 00 . 5 cos m 10 5.00 G 10 T 1 G 2000 4 2 2 4 m - - × = × = ( a ) For = 0 ° : ( 29 mWb 50 . 0 Wb 10 00 . 5 0 cos Wb 10 00 . 5 4 4 m = × = ° × = - - ( b ) For = 30 ° : ( 29 mWb 43 . 0 Wb 10 33 . 4 cos30 Wb 10 00 . 5 4 4 m = × = ° × = - - ( c ) For = 60 ° : ( 29 mWb 25 . 0 Wb 10 50 . 2 cos60 Wb 10 00 . 5 4 4 m = × = ° × = - - ( d ) For = 90 ° : ( 29 0 cos90 Wb 10 00 . 5 4 m = ° × = - 6 Give the direction of the induced current in the circuit, shown on the right in Figure 28- 37, when the resistance in the circuit on the left is suddenly ( a ) increased and ( b ) decreased. Explain your answer. Determine the Concept The induced emf and induced current in the circuit on the right are in such a direction as to oppose the change that produces them (Lenz’s Law). We can determine the direction of the induced current in the circuit. Note that when R is constant, B in the circuit to the right points out of the paper.
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( a ) If R increases, I decreases and B in the circuit to the right decreases. Lenz’s law tells us that the induced current is counterclockwise. ( b ) If R decreases, I increases and B in the circuit to the right increases. Lenz’s law tells us that the induced current is clockwise. 32 A solenoid that has a length equal to 25.0 cm, a radius equal to 0.800 cm, and 400 turns is in a region where a magnetic field of 600 G exists and makes an angle of 50º with the axis of the solenoid. ( a ) Find the magnetic flux through the solenoid. ( b ) Find the magnitude of the average emf induced in the solenoid if the magnetic field is reduced to zero in 1.40 s. Picture the Problem We can use its definition to find the magnetic flux through the solenoid and Faraday’s law to find the emf induced in the solenoid when the external field is reduced to zero in 1.4 s. ( a ) Express the magnetic flux through the solenoid in terms of N , B , A , and θ : π φ cos cos 2 m R NB NBA = = Substitute numerical values and evaluate m : ( 29 ( 29 ( 29 mWb 1 . 3 mWb 10 . 3 50 cos m 00800 . 0 mT 0 . 60 400 2 m = = ° = ( b ) Apply Faraday’s law to obtain: mV 2 . 2 s 1.40 mWb 3.10 0 m = - - = - = t ε 36 •• A 30.0-cm long rod moves steadily at 8.00 m/s in a plane that is perpendicular to a magnetic field of
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E2HWCH28 - Chapter 28 Magnetic Induction 20 A uniform...

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