Question 59 of 153

The figure shows a circular area of tthe radius $R$ where a uniform magnetic field $\vec{B}$ is going into the plane of the 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 $E(r)$?

ABCD

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Answer: (A)

$E=\dfrac{d\phi }{dt}=A\dfrac{dB}{dt}$
for
$r\lt R$, $E\left(2\pi r\right)=\pi {r}^{2}\dfrac{dB}{dt}\Rightarrow E\alpha r$
for
$r\gt R$, $E\left(2\pi r\right)=\pi {R}^{2}\dfrac{dB}{dt}\Rightarrow E\alpha \dfrac{1}{r}$