A thin infinitely large sheet lying in yz plane carries a current of linear current density `lambda`. The current is in negative y direction and `lambda` represents current per unit length measured along z-axis. Find the magnetic field near the sheet : (Magnetic field due to the sheet will be parallel to sheet)

(Long sheet with `lambda = ("current")/("length")`)

Options

A. `B = (mu_(0)lambda)/(2)`
B. `B = mu_(0)2lambda`
C. `B = mu_(0)lambda`
D. `B = (mu_(0)lambda)/(4)`

Answer

A

Explanation

`oint B.dl = mu_(0)Ien`
`underset(AB)int B.dl + underset(BC)int B.dl + underset(CD)int B.dl + underset(DA)int B.dl = mu_(0)I`
`0 + B.l + 0 + B. l + mu_(0)lambdaI`
`2Bl = mu_(0)lambdaI`
`B = (mu_(0)lambda)/(2)`