A small coil of radius r is placed concentrically at the centre of a much larger coplanar coil of radius R, with R≫r. Their mutual inductance is:
Options

Question

A small coil of radius r is placed concentrically at the centre of a much larger coplanar coil of radius R, with R≫r. Their mutual inductance is:

G1 Physics · Accepted Answer

For current I in the large loop, the field at its centre is B=µ₀I/(2R). Since r≪R, this field is nearly uniform over the small loop. Flux through the small loop is Φ=B·πr²=µ₀Iπr²/(2R). Hence M=Φ/I=µ₀πr²/(2R), so option B.