A toroid of mean radius is wound with closely and uniformly spaced turns carrying a…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetic materials
Electricity, Magnetism and Electromagnetism, Ch Magnetisation, bound currents and the auxiliary field H
Problem
A toroid of mean radius s=0.12m is wound with N=750 closely and uniformly spaced turns carrying a steady free current I=0.30A. The core is a linear magnetic medium of relative permeability μr=1200 filling the toroid completely; its cross-section is small compared with s, so all fields may be evaluated at the mean radius.
((a)) Find H, B and M in the core.
((b)) The core is now taken out of the winding and reshaped into a long straight cylinder of radius R=6.0mm. Idealise it as retaining a uniform magnetisation along its axis equal in magnitude to the M found in (a), with no free current anywhere. Find the bound surface current per unit length on its curved side, and the magnitude of B deep inside it.
((c)) A thin ring is now sliced from that cylinder, of axial thickness t=0.50mm and the same radius R=6.0mm, still with the same uniform axial magnetisation. Treating its bound surface current as a single circular loop of current, find that current and the magnitude of B at the centre of the ring.
((d)) For comparison, an identical cylinder of insulating material is instead uniformly polarised along its axis with P=3.0×10−6Cm−2. Find the magnitude of the bound surface charge density on one flat end face and on the curved side.
((e)) State which currents are the sources of B in part (b), and what H is deep inside that long cylinder.