Two conducting square loops of side lengths a and b ( a b ) are placed in the same plane with their centers coinciding. The mutual inductance between them is:

Step-by-step solution

Let a current i flow in the outer square loop of side length b . The perpendicular distance from the center to any side of the outer loop is d = b 2 . The magnetic field at the center due to one side of the square loop is given by the formula for a finite straight wire: B₁ = ₀ i 4 d ( ₁ + ₂) Here, ₁ = ₂ = 45^ and d = b 2 . B₁ = ₀ i 4 (b/2) ( 45^ + 45^ ) = ₀ i 2 b ( 1 2 + 1 2 ) = ₀ i 2 b ( 2 2 ) = 2 ₀ i 2 b The total magnetic field at the center due to all four sides is: B = 4 B₁ = 4 2 ₀ i 2 b = 2 2 ₀ i b Since a b