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

Answer

D

Explanation

Net magnetic field,m `B = sqrt(B_(1)^(2) + B_(2)^(2))`

`= sqrt(((mu_(0) I_(1))/(2pi d))^(2) + ((mu_(0) I_(2))/(2pi d))^(2))`
`( :' B_(1) = (mu_(0) I)/(2pi d)` and `B_(2) = (mu_(0) I_(2))/(2pi d))`
`= (mu_(0))/(2pi d) sqrt(I_(1)^(2) + I_(2)^(2))`