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A cylindrical region of uniform magnetic field exists perpendicular to the plane of the paper is increasing at a constant rate $\frac{d B}{d t} = α$ . A rod is placed along the diameter of the cylinder. Induced emf between the ends of the rod is

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$\frac{π α l^{2}}{2}$

$π α l^{2}$

$\frac{π α l^{2}}{4}$

zero

answer is D.

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Detailed Solution

Consider a cylindrical region of uniform magnetic field exist perpendicular to the plane of paper.

$E ⊥ d l$ at every point to the plane of paper.

So, $∆ V_{A B} = E d l \cos 90 ° = z e r o$

Thus, induced emf between the ends of the rod is zero.

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