A circular current loop of radius R is placed inside square loop of side length L(L >> R) such that they are co-planar and their centers coincide. The permeability of free space is ₀ . The mutual inductance between circular loop and square loop is _______.

Step-by-step solution

Using the reciprocity theorem, assume a current I flows through the larger square loop and compute the flux through the smaller circular loop. The mutual inductance is given by M = I . Magnetic field at the centre of the square loop: For a square of side L , the perpendicular distance from the centre to any side is d = L 2 , and each side subtends angles ₁ = ₂ = 45^ at the centre. The field due to one finite straight segment is: B_ segment = ₀ I 4 d ( ₁ + ₂) B_ segment = ₀ I 4 L 2 ( 1 2 + 1 2 ) = ₀ I 2 L 2 = 2 , ₀