Two conducting circular loops of radii R₁ and R₂ are placed in same plane with their centers coinciding. If R₁ > R₂ and current I is flowing through the circular loop of radius R₁ , then mutual inductance between them is proportional to

Step-by-step solution

Magnetic field at the center of the larger loop of radius R₁ carrying current I is given by B = ₀ I 2 R₁ Since R₁ > R₂ , the magnetic field can be considered approximately uniform over the entire area of the smaller loop. Magnetic flux linked with the smaller loop of radius R₂ is = B A₂ = ( ₀ I 2 R₁ ) ( R₂^2) The mutual inductance M is given by M = I = ₀ R₂^2 2 R₁ Therefore, M R₂^2 R₁ Answer: R₂^2 R₁