A time varying magnetic field `B=krt` (where k is a constant r is the radial distance from centre O) is existing in a circular region of radius R as shown. If induced electric field at `r=(R)/(2)` is `E_(1)` and at r=2R is `E_(2)` then the ratio `(E_(2))/(E_(1))` is

Options

A. 6
B. 4
C. 2
D. 1

Answer

C

Explanation

When `r le R`
`E2pir=(d)/(dt)underset(0)overset(r)intB2pirdr`
`Er=(d)/(dt)((ktr^(3))/(3))`
`E=-(kr^(3))/(3)`, when `r le R`
when `r gt R`
`E2pir=(d)/(dt)(underset(0)overset(R)intB2pirdr)`
`Er=(d)/(dt)(underset(0)overset(R)krtrdr)`
`E=(kR^(3))/(3r)` where r gt R
`therefore` at `r=(R)/(2),E_(1)=(kR^(2))/(12)`
at `r=2R,E_(2)=(kR^(2))/(6)`
`therefore(E_(2))/(E_(1))=2`