The figure shows a non conducting ring of radius `R` carrying a charge `q`. In a circular region of Radius `r`, a uniform magnetic field `B` perpendicular to the plane of the ring varies at a constant rate `(dB)/(dt)=beta`. The torque on the ring is

Options

A. `1/2qr^2beta`
B. `1/2qR^2beta`
C. `qr^2beta`
D. zero

Answer

A

Explanation

`El=(dphi)/(dt)=S(dB)/(dt)`
`E(2pir)=(pir^2)(beta)`
`:. E=r^2/(2R)betaimplies F=qE`
and `tau=FR=qER =1/2qr^2beta`