Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current I₁ and COD carries a current I₂. What will be the magnetic field on point lying at a distance d from O, in a direction perpendicular to the plane of the wires AOB and COD?

Solution

Given,
Two identical conducting wire AOB and COD are placed at right angles to each other.

Current carried by AOB = I₁
Current carried by COD = I₂

Magnetic field on AOB , B₁= $\frac{μ_{0} I_{1}}{2 πd} (- j)$
Magnetic field on COD, B₂ = $\frac{μ_{o} I_{2}}{2 πd} (+ i)$

Therefore,
Resultant magnetic field , B = $\sqrt{{B_{1}}^{2} + {B_{2}}^{2}}$

= $\frac{μ_{o}}{2 πd} \sqrt{{I_{1}}^{2} + {I_{2}}^{2}}$