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))/(2pid)(i_(1)+i_(2))`
B. `(mu_(0))/(2pid)(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 distance `a` above `O:`
`B_(1)=(mu_(0)i_(1))/(2pid)`
`B_(2)=(mu_(0)i_(2))/(2pia)`
`B_(1)` is `bot^(ar)` to `B_(2)`
Resultant of `B_(1)` and `B_(2)`
`B=sqrt(B_(1)^(2)+B_(2)^(2))=(mu_(0))/(2pid)sqrt(i_(1)^(2)+i_(2)^(2))`