Magnetic induction at point P from shown current-carrying long conductors is given by-

Options

A. `(5mu_(0)I)/(2sqrt(2)pir)(sqrt2-1)`
B. `(mu_(0)I)/(sqrt(2)pir)(sqrt2-1)`
C. `(8mu_(0)I)/(2pir)(sqrt2-1)`
D. `(mu_(0)I)/(4pir)(sqrt2-1)`

Answer

D

Explanation

`B = (mu_(0)i)/(4pid)[sin90^(@)-sin theta]`
`theta = 45^(@)`
`sin 45^(@) = (d)/(r)`
`B = (mu_(0)isqrt(2))/(4pir)[1-(1)/(sqrt(2))]`
`=(mu_(0)i)/(4pir)(sqrt(2)-1)`