(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.

Explanation

(a) Given relative permeability = `mu`,
Then permeability of iron `= mu _(0) mu`
Number of turns per meter = n
Current = I
Now `Deltat` center of salenoid cut an element of thickness dx at x meter from its centres So, number of turns in dx element is.
`N = ndx`
Now else, Bio Savart Law `B = (mu_(0)muNiR^(2))/((R^(2) + n^(2))^(3//2))`
let, K is the radius of circular path `= (mu_(0)mu_(i)dxR^(2))/((R^(2) + n^(2))^(3//2))`
After integration.
(b) (i) As we know that suscecptibility of a paramagnetic substances is positive (+ ve) though small. Here the given magnetic material is paramagnetic in nature.
(ii) When a.specimen of a paramegnetic substance is placed in a magnetic field, the magnetic field line prefer to pass through air thus, magnetic induction B inside the sample is more than the magnetic induction `B_(0)` outside the sample.