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
Two separate arrangements are to be compared. Arrangement 1. A thin disc-shaped permanent magnet has radius a=15mm and thickness t=3.0mm. Its magnetisation is uniform, of magnitude M=6.0×105Am−1, and points along the disc's axis, which we call +z. Because the disc is thin, treat the whole of its bound rim current as a single circular loop of radius 15mm lying in the plane of the disc. There is no free current anywhere in this arrangement. Arrangement 2. A toroid of mean radius s=60mm is wound uniformly with N=500 turns carrying a steady current I=0.40A. A linear magnetic material of relative permeability μr=250 fills the whole of the toroid's interior.
((a)) Find the total bound current that circulates round the curved rim of the disc.
((b)) Using the on-axis field of a circular current loop (Chapter 7), find the magnitude of B on the disc's axis at z=40mm from the centre of the disc.
((c)) Find the magnitude of H at that same axial point.
((d)) A long straight rod of the same material, with the same uniform M along its length, is made from the same magnet stock. Find B deep inside the rod.
((e)) For the toroid, find H and B at the mean radius.
((f)) Take a rectangle lying in a plane that contains the disc's axis, with one long side running along the axis from z=−100mm to z=+100mm, the opposite side parallel to it at 30mm from the axis, and two short sides joining their ends. Find the magnitudes of ∮B⋅dl and ∮H⋅dl round it, and explain why they differ.