Mutual Induction of a solenoid and a coil

AI Thread Summary
The discussion centers on calculating the induced electromotive force (emf) in a circular loop caused by the changing current in a coaxial solenoid. The solenoid has 1780 turns and a current that decreases linearly from 6.12 A to 1.46 A over 0.230 seconds. The mutual inductance formula and the rate of change of current are applied, but the user is struggling to arrive at the correct answer. Key variables include the solenoid's radius and length, as well as the loop's radius. Assistance is requested to identify the error in the calculations.
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Homework Statement



A single-turn circular loop of radius R = 0.235 m is coaxial with a long 1780 turn solenoid of radius 0.0435 m and length 0.850 m, as seen in the figure below. The variable resistor is changed so that the solenoid current decreases linearly from 6.12 A to 1.46 A in 0.230 s. Calculate the induced emf in the circular loop. (The field just outside the solenoid is small enough to be negligible.)

Homework Equations



M=N*∏*μ0*n*r^2

Vind = - N*∏*μ0*n*r^2 * di/dt

di/dt=(1.46-6.12)/0.23

The Attempt at a Solution



I used mutual inductance equ to find the potential difference induced

N is 1780, n=N/length, r=0.0435

but I still can't get the correct answer. I don't know where I did wrong here. Does anybody help me to find the answer? Thank you
 

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