Question

A long solenoid has $1000$ turns per metre and carries a current of $1\;{\text{A}}$ . It has a soft iron core of ${\mu _T} - 1000$ . The core is heated beyond the Curie temperature, ${T_C}$ .
This question has multiple correct options.
A. The H field in the solenoid is (nearly) unchanged but the B field decreases drastically.
B. The H and B fields in the solenoid are nearly unchanged.
C. The magnetism in the core reverses direction.
D. The magnetism in the core increases by a factor of about ${10^8}$ .

Answer 1

In a solenoid the magnetic field only depends on the number of turns and current through the solenoid. And the magnetic flux density depends on the relative permeability also.

Complete step-by-step solution:
The expression for the magnetic field inside the solenoid is given as,
$H = nI$
Where, $n$ is the number of turns, $I$ is the current through the solenoid.
And the expression for the magnetic flux density in the solenoid is given as,
$B = {\mu _0}{\mu _r}nI$
Where, ${\mu _0}$is the permeability of free space and ${\mu _r}$is the relative permeability.
The relative permeability can vary according to the temperature. Thus $B$ varies with temperature. Hence the $H$ field in the solenoid is (nearly) unchanged but the B field decreases drastically.
Let’s check the other options also.
And the option B is incorrect hence both $H$ and $B$ don’t change.
The temperature and the direction of the magnetic field are not related. So when the temperature increases to Curie temperature the direction is not reversed. Hence option C is incorrect.
The iron core of the solenoid is a Ferromagnetic material. When the Ferromagnetic material is raised beyond the Curie temperature, then it behaves like a paramagnetic material.
The magnetic susceptibility of the Paramagnetic material is given as, ${\left( {{\chi _m}} \right)_{para}} \approx {10^{ - 5}}$ and that of Ferromagnetic material is given as, ${\left( {{\chi _m}} \right)_{ferro}} \approx {10^3}$.
Therefore,
$\dfrac{{{{\left( {{\chi _m}} \right)}_{ferro}}}}{{{{\left( {{\chi _m}} \right)}_{para}}}} = \dfrac{{{{10}^3}}}{{{{10}^{ - 5}}}} \\\ = {10^8} \\\$
Thus ${\left( {{\chi _m}} \right)_{ferro}} = {10^8} \times {\left( {{\chi _m}} \right)_{para}}$

So when the temperature increases the core of the solenoid becomes paramagnetic and thus the magnetization diminishes by a factor of ${10^8}$.
Thus the option D is incorrect.
Option A is only correct.

Note:- We have to note that for Ferromagnetic materials the susceptibility will be always positive since they are strongly magnetized. The magnetic properties will change due to temperature. Hence the Ferromagnetic became paramagnetic.