Answer:
a) E(max)= 7.5398 v/m
b) B= 2 Tesla.
Explanation:
first we need to know the  law of faraday  look the attachment to see the formula.
if r<R where R= radius of supercondunting solenoid
E(2πr) =  -d * B(πr²) / dt
E= -Ï€/2*dB/dt
B(t)= 2+12sin(20Ï€t)
answer for A question:
dB/dt= 12(20Ï€) cos(20Ï€t)
E= -r/2 (12*20Ï€) cos(20Ï€t)
E= -120Ï€r cos(20Ï€t)
max electric field strenght at:
r=2cm
r=0.02m
E(max)= (120Ï€)*0.02)
E(max)= 7.5398 v/m
answer for question B:
value of B at the instant E reaches its maximum value
when
20πt = π, 3π, 5π,....
B= 2+12sinπ
B= 2 Tesla.
