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In Fig. a larger metal sheet of width w ...

In Fig. a larger metal sheet of width w carries a current I(uniformly distributed in its width w). Find the magnetic field at point P which lies on the plane of the sheet.

A

`(Qlambda)/(4piepsilon_(0))ln(2+sqrt(3))`

B

`(Qlambda)/(2piepsilon_(0))ln(2+sqrt(3))`

C

`(Qlambda)/(4piepsilon_(0))ln(2-sqrt(3))`

D

`(Qlambda)/(2piepsilon_(0))ln(2-sqrt(3))`

Text Solution

Verified by Experts

`dU=V_(P("ring"))lambdadx=(kQlambda)/(sqrt(R^(2)+x^(2)))dx`
`U=(Qlambda)/(4piepsilon_(0))int_(0)^(sqrt(3)R)(dx)/(sqrt(R^(2)+x^(2)))`
Let `x=R tan theta`
`rArr dx=R sec^(2)theta d theta`
If `x=0 rArr theta=0`, and `x=sqrt(3)R`
`rArr theta=pi//3`
`U=(Qlambda)/(4piepsilon_(0))int_(0)^(pi//3)sectheta d theta=(Qlambda)/(4piepsilon_(0))[ln(sectheta+tantheta)]_(0)^(pi//3)=(Qlambda)/(4piepsilon_(0))ln(2+sqrt(3))`
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