A circular coil of radius 'r' is placed on another circular coil whose radius is 'R' and the current flowing through it is changing and their centers coincide. ( R r ). If both the coils are coplanar, then the mutual inductance between them is proportional to

Step-by-step solution

Let the current in the larger coil of radius R be I . The magnetic field produced by the larger coil at its center is B = ₀ I 2R . Since R r , the magnetic field can be considered uniform over the entire area of the smaller coil. The magnetic flux linked with the smaller coil of radius r is = B A = ( ₀ I 2R ) ( r^2) . The mutual inductance M is given by M = I = ₀ r^2 2R . Therefore, M r^2 R . Answer: r^2 R