Two straight long conductors `AOB` and `COD` are perpendicular to each other and carry currents `I_(1)` and `I_(2)`. The magnitude of the magnetic induction at a point `P` at a distance `d` from the point `o` in a direction perpendicular to the plane `ABCD` is :

Options

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

Answer

C

Explanation

At `P: B_(net)=sqrt(B_(1)-B_(1))`
`=sqrt(((mu_(0))/(4pi) (2i_(1))/a)^(2)+((mu_(0))/(4pi) (2i_(2))/a)^(2))`
`=(mu_(0))/(2pia)(i_(1)^(2)+i_(2)^(2))^(1//2)`