Two identical conducting wires `AOB and COD` are placed at right angles to each other. The wire `AOB` carries an electric current `I_(1) and COD` carries a current `I_(2)`. The magnetic field on a point lying at a distance `d` from O, in a direction perpendicular to the plane of the wires `AOB and COD`, will be given by

Options

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

Answer

C

Explanation

Magnetic field due to wires at distance `d` above `O`
`B_(1)=(mu_(0)I_(1))/(2pid), B_(2)=(mu_(0)I_(2))/(2pid)`
`B_(1)` and `B_(2)` are perpendicular
`B_(P)=sqrt(B_(1)^(2)+B_(2)^(2))=(mu_(0))/(2pid) (I_(1)^(2)+I_(2)^(2))^(1//2)`