I have entered attempted this problem mulitple times and either get .0196 volts

Question

I have entered attempted this problem mulitple times and either get .0196 volts or .00392 volts and my homework software tells me this is wrong.

013 10.0 points A coil with N 23 turns and radius r 7.47 cm surrounds a long solenoid of radius m2 580 m (see 2.71 cm and the figure below). The current in the solenoid changes as I Io sin(wt), where I 5 A and w 120 rad/s. H A1 A2 NOE Inside solenoid has Na turns Outside solenoid has N1 turns What is the magnitude of the induced emf, EAB, across the 23 turn coil at t 1000 s? Answer in units of V

Explanation / Answer

here,

the mutual inductance , M = u0 * n * N * area * ur

M = 1.26 * 10^-6 * 23 * 580 * pi * 0.0747^2

M = 294.5 * 10^-6 H

the EMF induced in 24 turns coil , EMF = - M * di/dt

EMF = - 294.5 * 10^-6 * d(5 * sin(120 * t))

EMF = - 176700 * 10^-6 * cos(120 * t)

at t = 1000 s

EMF = - 0.176700 * cos(120 * 1000)

EMF = 0.08835 V

the magnitude of the EMF induced is 0.08835 V

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