Two identical coaxial circular loops, each of radius R , are placed at a separation of 2R . If both loops carry the same current I in the same direction, the magnitude of the net magnetic field at the exact midpoint of their common axis is:

Step-by-step solution

Let the two loops be placed coaxially with a separation of 2R . The midpoint of their common axis is at a distance x = R from the centre of each loop. The magnetic field produced by one loop at a distance x on its axis is given by: B = ₀ I R^2 2(R^2 + x^2)^ 3/2 Substituting x = R : B₁ = ₀ I R^2 2(R^2 + R^2)^ 3/2 = ₀ I R^2 2(2R^2)^ 3/2 = ₀ I R^2 2(2 2 R^3) = ₀ I 4 2 R Since the currents in both loops flow in the same direction, the magnetic fields produced by them at the midpoint point in the same direction. By the