For a ferromagnetic material,the relative permeability $(\mu_r)$ versus magnetic intensity $(H)$ has the following shape:

$A$ bar magnet is placed with its north pole pointing towards the geographic north. The magnetic field at a point $P$ on its equatorial line is zero. If the magnet is rotated by $90^\circ$,what will be the magnetic field at point $P$? The horizontal component of the Earth's magnetic field is $B_H$.

Answer the following questions:
$(a)$ Why does a paramagnetic sample display greater magnetisation (for the same magnetising field) when cooled?
$(b)$ Why is diamagnetism, in contrast, almost independent of temperature?
$(c)$ If a toroid uses bismuth for its core, will the field in the core be (slightly) greater or (slightly) less than when the core is empty?
$(d)$ Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields?
$(e)$ Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?
$(f)$ Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetisation of a ferromagnet?

Two identical bar magnets are fixed with their centres at a distance $d$ apart. $A$ stationary charge $Q$ is placed at $P$ in between the gap of the two magnets at a distance $D$ from the center $O$ as shown in the figure.

Two magnets of equal mass are joined at right angles to each other as shown. Magnet $1$ has a magnetic moment $3$ times that of magnet $2$. This arrangement is pivoted so that it is free to rotate in the horizontal plane. In equilibrium,what angle will magnet $1$ subtend with the magnetic meridian?

Match the items in List-$I$ with the items in List-$II$:
| List-$I$ | List-$II$ |
| :--- | :--- |
| $(A)$ High retentivity | $(i)$ Telephone diaphragm |
| $(B)$ High resistivity | (ii) Diamagnet |
| $(C)$ Low coercivity | (iii) To decrease eddy current losses |
| $(D)$ Negative susceptibility | (iv) Permanent magnet |