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A circular conducting loop of radius $r_{0}$ 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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Current induced in the loop is $I = \frac{B v}{π λ}$

EMF induced in the loop as a function of time is $e = 2 ν B [r_{0} - \frac{v t}{π}]$

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

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

answer is A, B, D.

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Detailed Solution

$L = 2 π r_{0} - 2 v t \Rightarrow r = \frac{2 π r_{0} - 2 v t}{2 π}$

$ε = \frac{d ϕ}{d t} = 2 B v (r_{0} - \frac{V t}{π}) \Rightarrow i = \frac{B v}{π λ}$

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