Question

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 the point P at a distance r from the centre of the circular region

(a) is zero

(b) decreases as 1/r

(c) increases as r

(d) decreases as 1/r2.

Answer 1

Correct Answer is: (b) decreases as 1/r

Construct a concentric circle of radius r. The induced electric field (E) at any point on this circle is equal to that at P. For this circle,

∮ Vector E. d Vector r = 2πrE = induced emf = dΦ/dt = πa2 B(t).

As the RHS is independent of r, therefore E ∝ 1/r.