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A time varying magnetic field B = Kr^(3)...

A time varying magnetic field `B = Kr^(3)t` is existing in a cylindrical region of radius 'R' as shown (where k is a constant). The induced electric field 'E' at `r (R )/(2)` is

A

`(KR^(4))/(20)`

B

`(KR^(4))/(40)`

C

`(KR^(4))/(60)`

D

`(KR^(4))/(80)`

Text Solution

Verified by Experts

The correct Answer is:
D
Using Faraday's law
`E2pir = -(d)/(dt) [ - underset(0)overset(r )int B2pirdr]`
`= (d)/(dt) [ underset(0)overset(r )int Kr^(3)t2pirdr]`
`E2pir = (d)/(dt) (2pikt(r^(5))/(5))`
`E = (Kr^(4))/(5)`, when `r le R`
`:. At r = (R )/(2), E = (KR^(4))/(80)`
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