The straight long conductors AOB and COD are perpendicular to each other and carry current `i_(1)` and `i_(2)`. The magnitude of the magnetic induction at point P at a distance a from the point O in a direction perpendicular to the plane ACBD is

Options

A. `(mu_(0))/(2pi a) (i_(1) + i_(2))`
B. `(mu_(0))/(2pi a) (i_(1) - i_(2))`
C. `(mu_(0))/(2pi a) (l_(1)^(2) + l_(2)^(2))^(1//2)`
D. `(mu_(0))/(2pi a) (l_(1) l_(2))/((l_(1) + l_(2)))`

Answer

C

Explanation

At point P -
`B_("net") = sqrt(B_(1)^(2) + B_(2)^(2))`
`= sqrt((mu_(0) I_(1))/(2pia))^(2) + ((mu_(0) I_(2))/(2pi a))^(2)`
`= (mu_(0))/(2pi a) (i_(1)^(2) + i_(2)^(2))^((1)/(2))`