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Question:

Two identical circular loops, P and Q, each of radius r and carrying equal currents are kept in parallel planes having a common axis passing through O. The direction of current in P is clockwise and in Q is anti-clockwise as seen from O which is equidistant from the loops P and Q. Find the magnitude of the net magnetic field at 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|| = μ₀r²I/2(r²+r²)³/² = μ₀I/4√2r pointing towards P.
Hence magnetic field at point O = →BQ + →BP = μ₀I/2√2r towards P.