Question

The figure shows a solenoid carrying time varying current $I=I_{0}t$. On the axis of this solenoid a ring has been placed. The mutual inductance of the ring and the solenoid is $M$ and the self inductance of the ring is $L$. If the resistance of the ring is $R$ then the maximum current which can flow through the ring is equal to

• A. $\frac{(2M+L)I_0}{R}$
• B. $\frac{M{I}_0}{R}$
• C. $\frac{(2M-L)I_0}{R}$
• D. $\frac{(M+L)I_0}{R}$

Answer 1

The correct option is B $\frac{M{I}_0}{R}$

The flux linked with the ring due to solenoid is $MI$
$\varphi =MI=M{I}_{0}t$
Only mutual inductance will play a role as there is no factor affecting the self inductance.
Hence
$e=\frac{d\varphi }{dt}=M{I}_0$
Current $I=\frac{e}{R}=\frac{M{I}_0}{R}$
Hence option (B) is correct.