A closed current-carrying loop having a current I is having area A. Magnetic moment of this loop is defined as `vec(mu) = vec(IA)` where direction of area vector is towards the observer if current is flowing in anticlockwise direction with respect to the observer. If this loop is placed in a uniform magnetic field `vec(B)`, then torque acting on the loop is given by `vec(tau) = vec(mu) xx vec(B)`. Now answer the following questions:
Let ring in the above question is having a radius R and a charge Q is uniformly distributed over it. Ring is rotated with a constant angular velocity `(omega)` as mentioned above.
Torque acting on the ring due to magnetic force is

Options

A. `(QR^(2)omega B)/(2)`
B. `(QR^(2)omega B)/(2 omega)`
C. `(omega R^(2)B)/(2 pi)`
D. None of the above

Answer

A

Explanation

`=MB sin theta =IA B sin 90^(@)=(Q/T) AB`
`(Q)/(2 pi) omega pi R^(2)B=(Qomega R^(2)B)/(2)`.