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  4. Radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of r0 ms -1. If at any instant radius of the loop is r, then emf induced in the loop at that instant will be

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Q. Radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of $r_{0} \,ms ^{-1}$. If at any instant radius of the loop is $r$, then emf induced in the loop at that instant will be

Electromagnetic Induction

Solution:

$\frac{d r}{d t}=r_{0} $
$\Rightarrow \phi=B \pi r^{2}$
$\varepsilon=\frac{-d \phi}{d t}=-B \pi(2 r) \frac{d r}{d t}$
$\varepsilon=-2 \pi B r_{0}$