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° . The current in the loop after the rotation is

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° . The current in the loop after the rotation is (A) zero (B) (B π R2/L) (C) (2 B π R2/L) (D) (B π R2/2 L)

Tardigrade Admin · Accepted Answer

Initially, the current was zero, so self-induced flux was also zero. Now when we rotate the loop, the change in flux is

Δ ϕ = 2 π 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 π R^{2} \times B

.

i = \frac{2 π R ^{2} \times B}{L}

Q. 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 $18 0^{\circ}$ . The current in the loop after the rotation is

zero

$\frac{B π R ^{2}}{L}$

$\frac{2 B π R ^{2}}{L}$

$\frac{B π R ^{2}}{2 L}$

Q. 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∘ . The current in the loop after the rotation is

zero

LBπR2​

L2BπR2​

2LBπR2​

Q. 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 $18 0^{\circ}$ . The current in the loop after the rotation is

$\frac{B π R ^{2}}{L}$

$\frac{2 B π R ^{2}}{L}$

$\frac{B π R ^{2}}{2 L}$