(a) Expression for Ampere's circuital law
Derivation of magnetic field inside the ring
(b) Identification of the material
Drawing the modification of the field pattern
(a)From Ampere's circuital law, we have,
......(i)
For the field inside the ring, we can write


$\therefore \mathit{B}.2\mathit{\pi }\mathit{r}={\mathit{\mu }}_0{\mathit{\mu }}_{\mathit{r}}\cdot \left(\mathit{n}.2\mathit{\pi }\mathit{r}\right)\mathit{I}$
$\therefore \mathit{B}={\mathit{\mu }}_0{\mathit{\mu }}_{\mathit{r}}\mathit{n}\mathit{I}$
(b) The material is paramagnetic. The field pattern gets modified as shown in the figure below.