The very long cylindrical solenoid of Figure P29.27 has a radius 0.50m and 1000

Question

The very long cylindrical solenoid of Figure P29.27 has a radius 0.50m and 1000 windings per meter along its length. A circular conducting loop of radius 1.0 m encircles the solenoid, with the long central axis of the solenoid passing through the center of the loop, and with the area vector of the loop parallel to the solenoid axis. The solenoid initially carries a steady current I, but the current is then reduced to zero during a 0.100-s time interval. If the average emf induced in the loop during that interval is 0.10 V, what was the initial current magnitude?

Explanation / Answer

magnetic field B = uo*n*I

magetic flux = B*A = uo*n*I*A

A = pi*r^2

r = 0.5 m

induced emf = e =rate of change in flux

e = (d/dt)*(B*A) = uo*n*pi*r^2*(dI/dt)

dI = I2 - I1

I 2= 0

dI = I

dt = 0.1

given e = 0.1

0.1 = 4*pi*10^-7*1000*pi*0.5^2*I/0.1

I = 10.13 A

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