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+I_2)`
C. `(mu_0)/(2pid)(I_1^2-I_2^2)`
D. `(mu_0)/(2pid)(I_1^2+I_2^2)^(1//2)`

Answer

D

Explanation

`B_1=(mu_0)/(2pi)I_1/d` acting in the plane of paper downwards.
`B_2=(mu_0)/(2pi)I_2/d` acting in the plane of paper towards right.
`:. B=sqrt(B_1^2+B_2^2)=(mu_0)/(2pid)(I_1^2+I_2^2)^(1//2)`