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 sqrtt`
D. E is constant

Answer

D

Explanation

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

Then change in flux : `dphi=(2pirdr)B`
`rArr e=(dphi)/(dt)=2pir((dr)/(dt))k/r`
`rArr e=2pick ("constant") [therefore (dr)/(dt)=c,B=k/r]`