Two straight long conductors `AOB` and `COD` are perpendicular to each other and carry currents `I_(1)` and `I_(2)`. The magnitude of the magnetic induction at a point `P` at a distance `d` from the point `o` in a direction perpendicular to the plane `ABCD` is :

Options

A. `(mu_(0)sqrt(i_(1)^(2)+i_(2)^(2)))/(2 pi d) `
B. `(mu_(0)(i_(1)+i_(2)))/(2 pi d)`
C. `(mu_(0)(i_(1)-i_(2)))/(2 pi d) `
D. `(mu_(0)sqrt(i_(1)^(2) - i_(2)^(2)))/(2 pi d) `

Answer

A

Explanation

Magnetic field intensity due to a long wire carrying current I at a distance d from the wire is given by `B = (mu_(0)I)/(2 pi d)` and its direction is perpendicular to the plane containing wire and that point according to the right-hand palm rule. Here, both the wires are kept perpendicular to each other and hence their magnetic fields will also be perpendicular to each other. Net field can be written as follows:
`B - sqrt(B_(1)^(2) + B_(2)^(2)) = (mu_(0)sqrt(i_(1)^(2) + i_(2)^(2)))/(2 pi d) `
Thus, option (a) is correct.