Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The current through P and Q are I and 4 I respectively in clockwise direction as seen from O . The net magnetic field at O is:

Step-by-step solution

Two identical circular loops P and Q, each of radius r , are separated by distance r along their common axis. Current in P is I and in Q is 4I (both clockwise as seen from O). Point O is at the midpoint. The magnetic fields from each loop at O: B₁ = ₀ I R^2 2(R^2 + R^2)^ 3/2 (from P, pointing toward Q) B₂ = 4 ₀ I R^2 2(R^2 + R^2)^ 3/2 (from Q, pointing toward P) B_ net = B₂ - B₁ = 3 ₀ I R^2 2(2R^2)^ 3/2 = 3 ₀ I 4 2 R Direction: towards Q.