Two identical long conducting wires AOB and Cod are placed at right angles to each other, with one above other such that O is their common point for the two. The wires carry `I_(1) and I_(2)` currents, respectively. Points P is lying at distance d form O along a direction perpendicular to the plane containing the wires. The magnetic field at the point P will be

Options

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

Answer

A

Explanation

`vecB_1 = (mu_0)/(4pi) (2I_1)/(d) (-hatj)`
`vecB_2 = (mu_0)/(4pi ) (2I_1)/(d) (hati) `
`B = sqrt(B_1^2 + B_2^2)`
` = (mu_0)/(2pi d) sqrt( I_1^2 + I_2^2) `