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  4. A uniform but time varying magnetic field B(t) exists in a circular region of radius R and directed into the plane of paper. The magnitude of induced electric field at a point P at a distance r (r > R) from the centre of the circular region is proportional to

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Q. A uniform but time varying magnetic field B(t) exists in a circular region of radius R and directed into the plane of paper. The magnitude of induced electric field at a point P at a distance r (r > R) from the centre of the circular region is proportional to

Solution:

$-\int E.dl = -\frac{d\phi}{dt}$
$E.2\pi r=\pi R^2.\frac{dB}{dt}$
$E = \frac {R^2}{2r}.\frac{dB}{dt}$
$\Rightarrow E \propto\frac{1}{r}$