A non-conducting ring having q uniformly distributed over its circumference is placed on a rough horizontal surface. A vertical time varying magnetic field `B = 4t^(2)` is switched on at time t = 0. Mass of the ring is m and radius is R.
The ring starts rotating after 2 s, the coefficient of friction between the ring and the table is

Options

A. `(4qmR)/(g)`
B. `(2qmR)/(g)`
C. `(8qR)/(mg)`
D. `(qR)/(2mg)`

Answer

C

Explanation

As, E `l=(dphi_(B))/(dt)`
or `E(2piR)=piR^(2).(dB)/(dt)=piR^(2)(8t)`
`therefore" "E=4Rt`
`F=qE=4qRt" [tangential]"`
`tau_(F)=4qR^(2)t`
`tau_(f)=(mumgR)`
When `tau_(F)gt tau_(f)`, ring will start rotating.
At t = 2 s,
`8qR^(3)=mumgR`
`therefore` Coefficient of friction, `mu=(8qR)/(mg)`