(a) An iron ring of relative permeability μ has windings of insulated copper wire of n turns per meter. When the current in the winding’s 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.

(a) Consider a ring of radius r having n turns per metre. Then total number of turns in the ring $=2\mathrm{\pi rn} = \mathrm{N}$
                          Current enclosed = NI = 2$\mathrm{\pi rnI}.$

By Ampere's circuital law, $\text{∮}\overrightarrow{\mathrm{B}}\cdot \overrightarrow{\mathrm{dl}}={\mathrm{\mu }}_0\mathrm{\mu r}$
$$\begin{gathered} \begin{array}{r}\mathrm{B}\times 2\mathrm{\pi r}={\mathrm{\mu }}_0\mathrm{\mu r}2\mathrm{\pi rnI} \\ \mathrm{or}\\ \mathrm{B}={\mathrm{\mu }}_0\mathrm{\mu rnI}\end{array} \end{gathered}$$
(b) Given, susceptibility, $\mathrm{\chi }=0.9853$
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: