A metallic wire is folded to form a square loop a side `'a'`. It carries a current `'I'` and is kept perpendicular to a uniform magnetic field. If the shape of the loop is changed from square to a circle without changing the length of thw wire and current, the amount of work done in doing so is

Options

A. (a) `Bia^(2)(1 - (4sqrt(3))/(9))`
B. (b) `Bia^(2)(1 - (sqrt(3))/(9))`
C. (c ) `(2)/(3) Bia^(2)`
D. (d) zero

Answer

A

Explanation

(a) Emf induced in coil, `epsilon = -(Deltaphi)/(Delta t) = - ((phi_(2) - phi_(1)))/(t_(2) - t_(1))`
`phi_(2) = BA_(2) - B (4a)/(2 xx 3) xx (4a)/(3) xx sin60^(@) = (4sqrt(3))/(9)Ba^(2)`
`phi_(1) = Ba^(2)`
Work done, `W = epsilonq = epsilonIDeltat = Ba^(2)(1 - (4sqrt(3))/(9))i`