(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Show that for a ferromagnetic material the field in the gap is given by?

**Physics Forums | Science Articles, Homework Help, Discussion**