# (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.

a) According to Ampere's circuital law, we have
$\oint B\cdot dl= \mu _{0}\mu _{r}I_{enclosed}$
Here it is an iron ring
so field inside the ring is,
$\oint B\cdot dl= B\int dl= B2\pi r$
where 'r' is the radius of the ring.
Given that number of turns per meter = n
So

$I_{enclosed}= 2\pi rn\, I$
Therefore

$B\cdot 2\pi r= \mu _{0}\mu _{r}\left ( 2\pi rn \right )I$
$B= \mu _{0}\mu _{r}nI$
b)
Given,
susceptibility of a magnetic material = 0.9853
For paramagnetic material the value of susceptibility  X is . $0< X< \varepsilon$
Where $\varepsilon$ is a small positive number
Here X is 0.9853 very small number so it is a paramagnetic material.
When paramagnetic material placed in a uniform magnetic field the field gives concentrated lines inside the material.

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