A conducting ring of radius r is placed perpendicular inside a time varying magnetic field as shown in figure. The magnetic field changes with time according to `B = B_0 + alphat` where `B_0` and `alpha` are positive constants. Find the electric field on the circumference of the ring.

Options

A. `-pi alpha r^2`
B. `-pialphar`
C. `-pi alpha^2r^2`
D. `-pialpha^2r`

Answer

A

Explanation

`phi=AB = pir^2 xx (B_0 + alphat)`
`(dphi)/(dt)=pir^2 d/(dt)(B_0 +alphat)`
`therefore (dphi)/(dt)=pir^2 (0+alpha)`
`therefore -epsilon=pir^2alpha`
`therefore epsilon=-pir^2alpha`