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 at a distance r from the centre of the circular region

Options

A. is zero
B. Decreases as `1/r`
C. Increases as r
D. Decreases as `1/r^(2)`

Answer

B

Explanation

When he is running with rod in horizontal position, no field is cut by the rod, so e = 0 Construct a concentric circle of radius r. The induced electric field (E) at any point on the circle is equal to that at P . For this circle
`oint vecE.vecd| = |(dphi)/(dt)| = A|(dB)/(dt)|`
or `E xx (2pir) = pia^(2).|(dB)/(dt)|`
`rArr E = a^(2)/(2r) |(dB)/(dt)| rArr E prop 1/r`