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) :Copper wire windings on the iron ring forms a toroid.
Magnetic field due to a toroid is given by $B=\mu nI$
where $\mu$ is the permeability of the medium, $n$ is the number of turns per unit length and $I$ is the current flowing.
Also, $\mu ={\mu }_r{\mu }_o$
$⟹B={\mu }_r{\mu }_{o}nI$
(b) : Susceptibility of the magnetic material is given as $\chi =0.9853$
Since the magnetic susceptibility of paramagnetic material is positive. So the given substance must be a paramagnetic material.