A circular current loop of radius R is placed inside a square loop of side length L (L R) such that they are co-planar and their centres coincide. The permeability of free space is μ₀. The mutual inductance between the circular loop and the square loop is _.

Question

A circular current loop of radius R is placed inside a square loop of side length L (L >> R) such that they are co-planar and their centres coincide. The permeability of free space is μ₀. The mutual inductance between the circular loop and the square loop is _.

Accepted Answer

(4) 2√2(μ₀R²)/L. The square of side L produces B=(2√2μ₀I)/(π L) at its centre. M=(Bπ R²)/I=(2√2μ₀R²)/L.

A circular current loop of radius R is placed inside a square loop of side length L (L >> R) such that they are co-planar and their centres coincide. The permeability of free space is μ₀. The mutual inductance between the circular loop and the square loop is _____.

Step-by-step solution