1. The problem statement, all variables and given/known data A toroidal shaped magnetic material of radius, a, and cross sectional radius R has a small transverse gap cut into it of length l. The toroid is uniformly overwound with a coil of N loops carrying a current I. Show that for a ferromagnetic material the field in the gap is given by B~mu0 N I/l [5 marks] 3. The attempt at a solution Assume that the curvature is small, so that locally B, H and M are parallel to each other, uniform across the cross-section and tangential. A circular loop integral of radius R will have the same value of H at every point, so: the loop integral of H.dl=H 2 pi R=NI H=NI/2 piR 2 pi R is the circumference, so for a toroid with a gap of length l: H=NI/l B=mu0(H+M) M=0 because the gap is made of empty space B=mu0 (H+0) =mu0 NI/l Have I gone wrong somewhere by saying something that's not true? I'd be grateful if you could help please.