Question

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

Answer 1

Field due to loop `P=(mu O I r^(2))/(2(r^(2)+r^(2))^(3//2))`(downwards)
Field due to loop `Q=(mu_(o)2Ir^(2))/(2(r^(2)+r^(2))^(3//2))` (downward)
So, net field at O will be downward
`=(mu_(o) Ir^(2))/(2(2r^(2))^(3//2))+(mu_(o)2Ir^(2))/(2(r^(2)+r^(2))^(3//2))`
`=(mu_(o)Ir^(2))/((2r^(2))^(3//2))((1)/(2)+2)=(5 mu_(o)Ir^(2))/(2^(3//2)r^(3))`.