Question

A superconducting loop of radius $R$ has self-inductance $L$ . A uniform and constant magnetic field $B$ is applied perpendicular to the plane of the loop. Initially current in this loop is zero. The loop is rotated by $180^\circ $ . The current in the loop after the rotation is

• A. zero
• B. $\frac{B \pi R^{2}}{L}$
• C. $\frac{2 B \pi R^{2}}{L}$
• D. $\frac{B \pi R^{2}}{2 L}$

Answer 1

Answer: (C)

Initially, the current was zero, so self-induced flux was also zero. Now when we rotate the loop, the change in flux is
$\Delta \phi=2\pi R^{2}\times B$
Finally, to maintain the same zero flux, the current in the superconducting loop will be such that the flux due to induced current will negative of the flux due to external field
$L\times i=2\pi R^{2}\times B$ .
$i=\frac{2 \pi R^{2} \times B}{L}$