A circular conducting loop of Radius $' r_{o}'$ and having resistance per unit length $' λ'$ as shown in the figure is placed in a magnetic field $B$ which is constant in space and time. The ends of the loop are crossed and pulled in opposite directions with a velocity $' v'$ such that the loop always remains circular and the radius of the loop goes on decreasing then

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Radius of the loop changes with $r = r_{0} - \frac{v t}{π}$

EMF induced in the loop as a function of time is $2 B v (r_{0} - \frac{v t}{π})$

Current induced in the loop is $\frac{B v}{2 π λ}$

Current induced in the loop is $\frac{B v}{π λ}$

answer is A, B, D.

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Detailed Solution

The length of the loop at any time is $l = 2 π r_{0} - 2 ϑ t$
$∴$ radius of the loop $= r_{0} - \frac{ϑ t}{π}$
$ε m f$ induced $= \frac{- d}{d t} (B π r^{2}) = 2 B ϑ (r_{0} - \frac{ϑ t}{π})$
$∴$ induced current $= \frac{e m f}{l λ} = \frac{B ϑ}{π λ}$