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  4. Figure shows a circular area of radius R where a uniform magnetic field vecB is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

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Q. Figure shows a circular area of radius R where a uniform magnetic field $\vec{B}$ is going into the plane of paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?Physics Question Image

JEE MainJEE Main 2014Electromagnetic Induction

Solution:

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$B = B _{0} t $
$r >\, R $
$\phi \bar{\varepsilon} \cdot de =\frac{ d \phi}{ dt }$
$\Rightarrow \varepsilon(2 \pi r )= B \pi r ^{2}$
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$e \propto r$
$r >\, R$
$\varepsilon(2 \pi r )= B \pi R ^{2}$
$\varepsilon \propto \frac{1}{r}$