Two identical circular current loops carrying equal currents are placed with their axes inclined at 45^ to each other as shown in the figure. The resultant magnetic field at P is

Step-by-step solution

The magnetic field at a point on the axis of a circular current loop is given by: B = ₀ I R^2 2(R^2 + x^2)^ 3/2 where R is the radius of the loop and x is the distance from the center to the point. For both loops, the distance from the center to point P is x = 3 R . Substituting this value: B₁ = B₂ = ₀ I R^2 2(R^2 + ( 3 R)^2)^ 3/2 = ₀ I R^2 2(R^2 + 3R^2)^ 3/2 = ₀ I R^2 2(4R^2)^ 3/2 = ₀ I R^2 2(8R^3) = ₀ I 16R Let the magnetic field due to the first loop be B ₁ . Based on the geometry, its axis is along the x-axis,