Question

A highly conducting ring of radius $R$ is perpendicular to and concentric with the axis of a long solenoid as shown in fig. The ring has a narrow gap of width $d$ in its circumference. The solenoid has cross sectional area $A$ and a uniform internal field of magnitude $B_0$. Now beginning at $t=0$,the solenoid current is steadily increased so that the field magnitude at any time $t$ is given by $B\left(t\right)=B_0+\alpha$ where $\alpha >0$. Assuming that no change can flow across the gap, the end of ring which has excess of positive charge and the magnitude of induced e.m.f in the ring are respectively

• A. $X,A\alpha$
• B. $X,\pi R^2\alpha$
• C. $Y,\pi A^2\alpha$
• D. $Y,\pi R^2\alpha$

Answer 1

The correct option is A $X,A\alpha$

Since the current is increasing, so inward magnetic flux linked with the ring also increasing (as viewed from left side). Hence induced current in the ring is anticlockwise, so end x will be positive

Induced emf $|e|=A\frac{dB}{dt}=A\frac{d}{dt}(B_o+\alpha t)$

$|e|=A\alpha$