Two identical circular loops, P and Q, each of radius r and carrying currents I and 2 I respectively are lying in parallel planes such that they have a common axis. The direction of current in both the loops in clockwise as seen from O, which is euqidistant from both loops. Find the magnitude of the net magnetic field at point O.

Explanation

The point O lies at the axial line of both the current carrying loops at a distance x = r from centre of either loop.
`:.` Magnetic field due to coil P, `B_P = (mu_0 I Nr^2)/(2[r^2 + r^2]^(3//2)) = (mu_0 I N)/(4sqrt(2)r)` along QP
and magnetic field due to coil Q, `B_Q = (mu_0 (2I)Nr^2)/(2[r^2 + r^3]^(3//2)) = (mu_0 I N)/(2sqrt(2) r)` along PQ
As `B_P and B_Q` are in mutually opposite directions, hence net magnetic field at point Q
`B = B_Q - B_P = (mu_0 I N)/(4sqrt(2) r)` along `PQ`