A time varying uniform magnetic field passes through a circular region of radius R. The magnetic field is directed outwards and it is a function of radial distance 'r' and time 't' according to relation B-B_(0)rt. The induced electric field strength at a radial distance `R//2` from the centre will be.

Options

A. `(B_(0)R^(2))/(12)`
B. `(B_(0)R^(2))/(6)`
C. `(2B_(0)R^(2))/(3)`
D. `(B_(0)R^(2))/(16)`

Answer

A

Explanation

`phi =underset(o)overset(R//2)intB(2pir)dr=B_(0)t2pi(r^(3)/(3)) _(0)^(R//2) =B_(0)(2pi)(1)/(3)(R^(3)/(8))t`
`thereforeE(2pi((R)/(2)))=(-dphi)/(dt)=-B_(0)(2pi)R^(3)/(24)`
`impliesE=(B_(0)R^(2))/(12)`