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. (a)4 B
B. (b)`sqrt(2)B`
C. (c) `2sqrt(2)B`
D. (d) Zero

Answer

3

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_(2))^(2)+(B_(3)+B_(4))^(2))`