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A solenoid carries a current that increases linearly with time, I = I0 t (I0 constant). A conducting ring of self-inductance L and resistance R is placed coaxially on the solenoid's axis; the mutual inductance between ring and solenoid is M. Find the maximum (steady) current that flows in the ring.

1. (2M + L) I0 / R
2. M I0 / R
3. (2M - L) I0 / R
4. (M + L) I0 / R

Correct answer: M I0 / R

Solution

EMF in ring = M dI/dt = M I0 (constant). Once a steady ring current is reached, dI_ring/dt = 0, so the self-inductance term L dI_ring/dt vanishes. The maximum (steady) ring current is then simply emf/R = M I0 / R.

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