Question

The diagram shows a solenoid carrying a time-varying current, $I=I_{0}t$ . On the axis of this solenoid, a ring has been placed as shown in the figure at the right. 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 maximum current which can flow through the ring is,

• A. $\frac{\left(\right. 2 M + L \left.\right) I_{0}}{R}$
• B. $\frac{M I_{0}}{R}$
• C. $\frac{\left(\right. 2 M - L \left.\right) I_{0}}{A}$
• D. $\frac{\left(\right. M + L \left.\right) I_{0}}{R}$

Answer 1

Answer: (B)

Magnetic flux linking due to mutual inductance is $\phi=MI=MI_{0}t$
Hence, induced emf $\left|e\right|=\frac{d \phi}{d t}=MI_{0}$
Current through ring, $i=\frac{e}{R}=\frac{M I_{0}}{R}$ .