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. (a) `E prop t^(2)`
B. (b) `E prop t`
C. ( c) `E prop sqrt(t)`
D. (d) `E` is constant

Answer

D

Explanation

(d) 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) [`:.` `(dr)/(dt) = c, B = (k)/(r)]`
Then change in flux: `dphi = (2pidr)B`