Question

Two identical circular wires $P$ and $Q$ each of radius $R$ and carrying current ${}^{\prime }{I}^{\prime }$ are kept in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils.

Answer 1

The magnetic field would be in the direction perpendicular to the plane of coil for which magnetic field is calculated.

Hence magnetic field due to each coil is $\frac{{\mu }_{0}I}{2R}$ perpendicular to each other.

Hence the magnitude of resultant field is $\frac{\sqrt{2}{\mu }_{0}I}{2R}$

The net field would be inclined equally to both the fields.