Question

A thin non conducting ring of mass `m`, radius a carrying a charge `q` can rotate freely about its own axis which is vertical. At the initial moment, the ring was at rest in horizontal position and no magnetic field was present. At instant `t=0`, a uniform magnetic field is switched on which is vertically downward and increases with time according to the law `B=B_0t`. Neglecting magnetism induced due to rotational motion of ring.
Angular acceleration of ring is

Answer 1

(a) `B=B_(0)t`
`(dB)/(dt)=B_(0)`
`ointve(E).vec(dt)=(dphi)/(dt)=(d)/(dt)(B.pia^(2))E.2pia=((dB)/(dt))pia^(2)=B_(0).pia^(2)`
`E=(B_(0)a)/(2)` Flux is increse, Ewil be as shown
`tau=intdqE.a=qEa`
Torque about `O=1alpha=ma^(2)alpha`
`alpha=(qe)/(ma)=(qB_(0)alpha)/(2ma)=(qB_(0))/(2m)`