A long solenoid of radius a =10.0cm and length 15.0meters has N 1 = 3500 turns a

Question

A long solenoid of radius a =10.0cm and length 15.0meters has N1 = 3500 turns and carries a clockwise, variable current; at time t=1.00sec, the current is 30.0 A, and at time t=3.00sec, the current is 6.00 A. Inside the solenoid is a small, circular coil having N2=55 turns, having a radius of b=7.00cm, having a resistance R=20.0 ohms, and whose plane makes a fixed angle of 25.0 degrees with respect to the long axis of the solenoid.

a. Find the magnetic field B in the solenoid at the times t=1.00sec, and t=3.00sec.

b. Find the average EMF induced in the small coil.

c. Find the average induced current in the small coil; is the direction of the induced current in the small coil clockwise or counterclockwise?

Explanation / Answer

a) at t=1 sec, B= u0 I N/L = 4*pi*10^(-7)*30*3500/15=.008796 T at t=3 sec, B= u0 I N/L = 4*pi*10^(-7)*6*3500/15=.00176 T b) emf = d flux /dt = N A cos theta dB/dt = 55*cos(25)* pi * (7E-2)^2 * (.00176-0.008796)/2 =.0027 V c) I = V/R = 0.0027/20=1.35 E-4 A since there is a derease in the clockwise current and thus a decrease in the magnetic field, the smaller solenoid will try to increase the current and thus will have a clockwise current as well.

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