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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. The direction of current in both the loops is clockwise as seen from O which is equidistance from both loops. Find the magnitude of the net magnetic field at point O.

Solution:

Magnetic field at O due to P: ||→BP|| = μ₀r²I / 2(r² + r²)³/² = μ₀I / 4√2r pointing towards P.
Magnetic field at O due to Q: ||→BQ|| = μ₀r²(2I) / 2(r² + r²)³/² = 2μ₀I / 4√2r pointing towards Q.
Hence magnetic field at point O = →BQ − →BP = μ₀I / 4√2r towards Q