Two conducting circular loops are placed in the same plane with their centers coinciding. The outer loop has a radius R and the inner loop has a radius r , where r R . If the mutual inductance between the two loops is M , the radius r of the inner loop is given by:

Step-by-step solution

Let a current i flow in the outer loop of radius R . The magnetic field produced at the center of the loops is B = ₀ i 2 R . Since r R , the magnetic field can be assumed to be uniform over the entire area of the inner loop. The magnetic flux linked with the inner loop is = B r^2 = ( ₀ i 2 R ) r^2 . By the definition of mutual inductance, = M i . Equating the two expressions for flux: M i = ₀ i r^2 2 R M = ₀ r^2 2 R Rearranging to solve for r : r^2 = 2 M R ₀ r = 2 M R ₀ Answer: 2 M R ₀