A coil of wire having finite inductance and r | vedclass

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(D) Let $k_1, k_2, k_3, k_4, k_5$ be constants.The current in the $RL$ circuit is given by $I_1(t) = k_1(1 - e^{-t/	au})$.The magnetic field $B(t)$ a

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Passes through a maximum

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(D) Let $k_1, k_2, k_3, k_4, k_5$ be constants.The current in the $RL$ circuit is given by $I_1(t) = k_1(1 - e^{-t/	au})$.The magnetic field $B(t)$ at the axis of the coil is proportional to the current $I_1(t)$,so $B(t) = k_2 I_1(t) = k_2 k_1(1 - e^{-t/	au})$.The induced current $I_2(t)$ in the ring is proportional to the rate of change of magnetic flux,which is proportional to $dB(t)/dt$. Thus,$I_2(t) = k_3 \frac{dB(t)}{dt} = k_4 e^{-t/	au}$.Therefore,the product $I_2(t) B(t) = k_5 (1 - e^{-t/	au}) e^{-t/	au} = k_5 (e^{-t/	au} - e^{-2t/	au})$.At $t = 0$,$I_2(t) B(t) = 0$. As $t 	o \infty$,$I_2(t) B(t) 	o 0$. Since the product is positive for $t > 0$,it must pass through a maximum.

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