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 length of 100 cm, 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 is hooked to a voltmeter 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

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

magnetic flux through inner solenoid phi = N2*B*A2

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

r2 = D2/2 = 10/2 = 5 cm = 0.05 m

emf induced = rate of change in flux

emf = (d/dt)*(phi)

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

dI/dt = 60 milli amp/minute = 60*10^-3/60 = 10^-3 amperes/second

emf = (1000*500*10^-3*pi*0.05^2/10)*10^-3

voltmeter reading = 0.0004 volts

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.