What will be the resulatant field at the origin due to the four indinite length wires if each wire produces magnetic field `B` at origin ?

Options

A. `4 B`
B. `sqrt(2) B`
C. `2 sqrt(2) B`
D. Zero

Answer

C

Explanation

Direction of magnetic field `(B_(1). B_(2).B_(3)` and `B_(4)`) at origin due to wires `1,2,3` and `4` are shown in the following figure. `B_(1) = B_(2) = B_(3) = B_(4) = (mu_(0))/(4pi) (2i)/(x) = B`
So net magnetic field at origin `O`
`B_(net) = sqrt((B_(1) + B_(3))^(2) + (B_(2) + B_(4))^(2))`
`= sqrt((2B)^(2) + (2B)^(2)) = 2 sqrt(2) B`