A uniform but time-varying magnetic field $B (t)$ exists in a circular region of radius $a$ and is directed into the plane of the paper as shown. The magnitude of the induced electric field at point $P$ (outside the circular region) at a distance $r$ from the centre of the circular region

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∫ E → . d l → = | d ϕ d t | = A | d B d t | ⇒ E 2 π r = π a 2 d B d t for r ≥ a Therefore, E = a 2 2 r d B d t Therefore, the Induced electric field ∝ 1 r For r ≤ a E ( 2 π r ) = π r 2 | d B d t | or E = r 2 d B d t or E ∝ r At r = a, E = a 2 d B d t Therefore, the variation of E with r (distance from centre) will be as follows:

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