Figure shows a circular area of radius R where a uniform magnetic… | JEE Main 2014 (19 Apr, Shift 1)

Q31JEE Main 2014 · 19 APR · SHIFT 1Medium

Lenz's Law, Eddy Currents & Induced Electric Field

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)?

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Answer: (a)

Use $\oint \vec E\cdot d\vec l = \frac{d\phi}{dt}$ on a circle of radius $r$ .
Inside ( $r<R$ ): $E\,2\pi r = \pi r^2\frac{dB}{dt} \Rightarrow E = \frac{r}{2}\frac{dB}{dt}$ , linear in $r$ .
Outside ( $r>R$ ): $E\,2\pi r = \pi R^2\frac{dB}{dt} \Rightarrow E = \frac{R^2}{2r}\frac{dB}{dt}$ , falls as $\frac{1}{r}$ .
Straight rise to a peak at $r=R$ , then a $1/r$ decay. So the answer is (a).

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Lenz's Law, Eddy Currents & Induced Electric Field question from JEE Main 2014 (19 Apr, Shift 1)

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