A superconducting loop of the radius R has self-inductance L . A uniform and the constant magnetic field B is applied perpendicular to the plane of the loop. Initially current in this loop is zero. Th

Question

A superconducting loop of the radius R has self-inductance L . A uniform and the 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

TestHub · 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

$L \times i = 2 π R^{2} \times B$ .

$i = \frac{2 π R^{2} \times B}{L}$

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