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 rotation is equal to
A.
zero
B.
$$\frac{{B\pi {R^2}}}{L}$$
C.
$$\frac{{2B\pi {R^2}}}{L}$$
D.
$$\frac{{B\pi {R^2}}}{2L}$$
Answer :
$$\frac{{2B\pi {R^2}}}{L}$$
Solution :
Flux can’t change in a superconducting loop.
$$\Delta \phi = 2\pi {R^2}.B$$
Initially current was zero, so self flux was zero.
$$\therefore $$ Finally $$Li = 2\pi {R^2} \times B$$
$$i = \frac{{2\pi {R^2} \times B}}{L}$$
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A.
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