Two ideal solenoids are arranged concentrically in upright positions so that the

Question

Two ideal solenoids are arranged concentrically in upright positions so that their windings circle in opposite directions as viewed from above. The outer solenoid has a diameter of

20 cm and a leng th of 100cm, and consists of 1000 turns. It is hooked to a current source so the current enters the coil at the top and increases at 60 milliamps per minute. The inner solenoid has the same length, half the diameter, and half the turns. It ishooked to a volt meter such that the positive terminal is connected to the top. Both solenoids are immersed in a liquid with a magnetic permeability of 1 mT·m/A. Find the voltage the meter will show after the current has been activated

Explanation / Answer

diameter D = 20 cm

length L = 100 cm

dI/dt = 60 mA/min = 10^-3 A/second

magnetic field inside the outer solenoid B = u*N1/L*I

magnetic flux through inner solenoid phi = N2*B*A^2

phi = N2*u*N1*I*pi*r2^2 / L

r2 = D2/2 = 20/2 = 10 cm = 0.10 m

emf induced = rate of change in flux

emf = (d/dt)*(phi)

emf = (N1*N2*u*pi*r^2/L)*(dI/dt)

emf = (1000*500*10^-3*pi*0.10^2 / 1.0)*10^-3

voltmeter reading = 0.0157 volts

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