Two concentric coplanar circular coils have radii a and b, with b≫a, as shown. The inner coil has resistance R. Current in the outer coil is increased from 0 to i. Find the total charge that circulates through the inner coil.

Question

G1 Physics · Accepted Answer

Field at the centre due to the large loop is B≈µ₀i/(2b). Flux through the small loop is Φ=B·πa², so mutual inductance M=Φ/i=µ₀πa²/(2b). Total induced charge when current changes from 0 to i is q=ΔΦ/R=Mi/R=µ₀iπa²/(2Rb). Hence A.