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

Answer

B

Explanation

The magnetic field inductions at a point P, at a distance d from O in a direction perpendicular to the plane of the wires due to currents through AOB and COD are perpendicular to each other, is:

`B=sqrt(B_(1)^(2)+B_(2)^(2))=[((mu_(0))/(4pi)(2I_(1))/d)^(2)+((mu_(0))/(4pi)(21_(2))/d)^(2)]^(1//2)=(mu_(0))/(2pid)sqrt((I_(1)^(2)+I_(2)^(20))`