A circular coil of 17 turns and radius 14.9cm surrounds a long solenoid of radiu

Question

A circular coil of 17 turns and radius 14.9cm surrounds a long solenoid of radius 4.1cm and 1.00x103 turns per meter. The two are oriented so that the axis of the coil and the axis of the solenoid are parallel and the center of the coil is at the center of the solenoid. The current in the solenoid is 3.7A.

a) What is in Webers, the flux through the coil?

b) What would be in volts, the induced emf in the loop if the current in the solenoid is reduced to zero in 0.06 seconds?

The situation is reversed and our coil is placed such that it is surrounded by a long large solenoid of radius 2 x 14.9cm.

c) What is in Webers, the flux through the coil now? (use the same values for the other question variables)

Explanation / Answer

magnetic field inside the solenoid is

B = mu_o N I = ( 4 pi*10^ -7 ) ( 1000 ) ( 3.7 A ) = 4.69*10^-3 T

magnetic flux through the coil is

flux = B N A = ( 4.69*10^ -3 ) ( 17) pi (0.149 m)^2 = 0.0055 Wb

b)

emf induced in the loop is

e = flux / time = ( 0.0055 Wb ) / 0.06 s = 0.091 V

c)

Magnetic flux through the coil is

flux = B A

magnetic field inside the solenoid doesn't change and area of coil is same as in part (a). so flux is 0.0055 Wb

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