Question

You have two cylindrical solenoids, one inside the other, with the two cylinders concentric. The outer solenoid has length l(outer)=400 mm, radius R(outer)=50mm, and N(outer)=1000 windings. The inner solenoid has length l(inner)=40mm, radius R(inner)=20mm, and N(inner)=150 windings. The inner solenoid is centered within the outer solenoid. When the outer solenoid carries a current given by I(t)=I(0)sin(wt), with I(0)=600mA and w=100s^(-1), what is the peak emf in the inner solenoid?

Answer 1

magnetic field due to outer solenoid on the axis = mu * nI

n = number of turns per unit length = (1000/(400/1000)) =2500 per meter

I = current

flux through inner solenoid = flux due to own (not changing) + flux due to outer

rate of change of flux in inner solenoid => rate of change of flux due to outer solenoid

(mu * Iosin(wt) * n ) * area

maximum = (mu * Io * w * n) * area

area of 150 windins = 150 * pi R^2

=> (4pi*10^(-7)) * 600*10^(-3) * 100 * (2500) * (pi*(20/1000)^2 * 150 )

= 0.03553057584 V

= 35.53 mV