Question

(a) An iron ring of relative permeability ${\mu }_r$ has windings of insulated copper wire of n turns per metre. When the current in the windings is I, find the expression for the magnetic field in the ring.
(b) The susceptibility of a magnetic material is 0.9853. Identify the type of magnetic material. Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field.

Answer 1

(a) Consider a ring of radius r having n turns per metre, If n is the number of turns per metre, then total number of turns in the ring = perimeter times the number of turns
= $2\pi rn=N$

Current enclosed = Nl = 2$\pi$rn I.

By Ampere's circuital law, $\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_{0}I$

$B\times 2\pi r=\mu 2\pi rnI$

or $B=\mu nI$


(b) Given, susceptibility, x = 0.9853.

The material is paramagnetic in nature.

If a piece of this material is kept in uniform magnetic field, then field pattern gets modified as follows:


The lines of forces tend to pass through the material rather than the surrounding air.