A uniform circular loop of radius a and resistance `R` palced perpendicular to a uniform magnetic field `B`. One half of the loop is rotated about the diameter with angular velocity `omega` as shown in Fig. Then, the current in the loop is

Options

A. (a) zero, when `theta` is zero
B. (b) `(pia^(2)Bomega)/(2R)`, when `theta` is zero
C. ( c) zero, when `theta = pi//2`
D. (d) `(pia^(2)Bomega)/(2R)`, when `theta = pi//2`

Answer

A, D

Explanation

(a, d): `theta = omegat`. Only half circular part will be involved in inducing emf , so effective area `A = (pia^(2))/(2)`

`phi = BA cos theta`
`e = - (dphi)/(dt) = + BA sin theta ((dtheta)/(dt)) `rarr` e = (Bpia^(2))/(2)omega sin theta`
`I = (e)/(R ) = (Bpia^(2))/(2R)sin theta`
Clearly `I = 0`, when `theta = 0^(@)` and when `theta = (pi)/(2), I = (Bpia^(2)omega)/(2R)`