Question

Two identical circular coils, P and Q, carrying currents `1A` and `sqrt3A` respectively, are placed concentrically and perpendicular to each other lying in the XY and YZ plane. Find the magnitude and direction of the net magnetic field at the centre of the coils.

Answer 1

Correct Answer - `(mu_0)/(R)T` in X-Z plane
`B_P=(mu_0I_1)/(2R)=(mu_0xx1)/(2R)=(mu_0)/(2R)` acting along Z-axis
`B_Q=(mu_0I_2)/(2R)=(mu_0xxsqrt3)/(2R)=sqrt3/2(mu_0)/(R)`
acting along X-axis
Net magnetic field is
`B=sqrt(B_P^2+B_Q^2)=(mu_0)/(2R)[(1)^2+(sqrt3)^2]^(1//2)`
`=(mu_0)/(R)T` (in X-Z plane)