A time varying magnetic field is present in a cylindrical region of radius R as shown in figure (cross-sectional view). B is increasing with time at the rate of $α$ Tesla/sec, mark out the correct statement(s) for the given situation, ‘r’ being the distance from centre of cylindrical region

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For $r > R,$ the induced electrical field is proportional to $\frac{1}{r}$

If a coaxial non-conducting ring of radius R/2 is placed in the magnetic field region, then emf induced in the ring is $\frac{π α R^{2}}{4}$

For r = R, the induced electrical field is maximum

For $r < R,$ the induced electrical field is proportional to ‘r’

answer is A, B, C, D.

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Detailed Solution

$F o r r \leq R, E \times 2 π r = \frac{d B}{d t} \times π r^{2} \Rightarrow E = \frac{α r}{2}$

$F o r r > R, E \times 2 π r = \frac{d B}{d t} \times π R^{2} \Rightarrow E = \frac{α R^{2}}{2 r}$

$F o r r = \frac{R}{2} t h e e m f i n d u c e d . e = \frac{d B}{d t} \times π {(\frac{R}{2})}^{2} = \frac{π α R^{2}}{4}$

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