A solenoid 2.0 m long and 30 cm in diameter consists of 5000 turns of wire (prim

Question

A solenoid 2.0 m long and 30 cm in diameter consists of 5000 turns of wire (primary). A 5 turn coil (secondary) with negligible resistance is wrapped around the solenoid and connected to a 180 ohm resistor. The solenoid current is given by I = I_0 sin omegat where I_0 = 85 A,omega = 210 rad/s, and t is in seconds. A) Determine the magnetic field at the center of the solenoid (primary) at t = 1 ms. B) Determine the peak epsilonmf induced in the secondary loop. c) what is the current in the secondary coil when the primary coil current is a maximum?

Explanation / Answer

given data

L = 2m

d = 30 cm

N1 = 5000 turns

N2 = 5 turns

R = 180 ohms

I = Io*sin(w*t)

= 85*sin(w*t)

w = 210 rad/s

A) at t = 1 ms

B = mue*N1*I/L

= 4*pi*10^-7*5000*85*sin(210*1*10^-3)/2

= 0.0556 T

B) emf = A*N2*dB/dt

= (pi*d^2/4)*N2*mue*N1*Io*cos(w*t)*w/L

emf_peak = (pi*0.3^2/4)*5*4*pi*10^-7*5000*85*210/2

= 19.8 volts

C)
I_seconary = emf_peak/R

= 19.8/180

= 0.11 A

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