A flexible wire loop in the shape of a circle has a radius that grows linearly with time. There is a magnetic field perpendicular to the plane of the loop that has a magnitude inversely proportional to the distance from the centre of the loop, `B(r ) prop (1)/(r )` How does the `emf` `E` vary with time?

Options

A. `E prop t^(2)`
B. `E prop t`
C. `E prop sqrt(t)`
D. `E` is constant

Answer

D

Explanation

Let radius of the loop `r` at time `t` and in further time `dt`, radius increases by `dr`.

The change in flux: `d phi = (2 pi dr) B`
`rArr e = (d phi)/(dt) = 2pi r((d r)/(dt)) (k)/( r)`
`rArr e = 2pi c k ("constant") [ :. (d r)/(dt) = c, B = (k)/( r)]`