A long solenoid with turns per metre carries a steady free current

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 long solenoid with

n = 1200

turns per metre carries a steady free current

I = 0.50\,\mathrm{A}

. Its bore is completely filled, along its whole length, by a rod of linear magnetic material of relative permeability

\mu_r = 400

. Consider a point well inside, far from either end, where the fields are uniform and along the axis. A student writes: "Ampère's law says

\oint\mathbf{B}\cdot d\mathbf{l} = \mu_0 I_{\mathrm{enc}}

, and the current enclosed by the usual rectangular loop is just the winding current, so

B = \mu_0 n I = 7.5\times10^{-4}\,\mathrm{T}

, core or no core." ((a)) Find

H

well inside the solenoid. ((b)) Find

M

in the core and the bound surface current per unit length on its curved surface. ((c)) Find the true value of

B

, and state exactly what the quoted argument left out of

I_{\mathrm{enc}}