Two short bar magnets of length $1 \ cm$ each have magnetic moments $1.20 \ Am^2$ and $1.00 \ Am^2$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $20.0 \ cm$. The value of the resultant horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to (Horizontal component of Earth's magnetic induction is $3.6 \times 10^{-5} \ Wb/m^2$)

$(a)$ What happens if a bar magnet is cut into two pieces: $(i)$ transverse to its length,$(ii)$ along its length?
$(b)$ $A$ magnetised needle in a uniform magnetic field experiences a torque but no net force. An iron nail near a bar magnet,however,experiences a force of attraction in addition to a torque. Why?
$(c)$ Must every magnetic configuration have a north pole and a south pole? What about the field due to a toroid?
$(d)$ Two identical-looking iron bars $A$ and $B$ are given,one of which is definitely known to be magnetised. (We do not know which one.) How would one ascertain whether or not both are magnetised? If only one is magnetised,how does one ascertain which one? [Use nothing else but the bars $A$ and $B$.]

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Magnetic induction	$(I)$ Ampere meter$^2$
$(B)$ Magnetic intensity	$(II)$ Weber
$(C)$ Magnetic flux	$(III)$ Gauss
$(D)$ Magnetic moment	$(IV)$ Ampere meter

Choose the correct answer from the options given below:

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 with a length of $10 \, cm$ and a weight of $50 \, g$ are placed freely with their like poles facing each other in an inverted vertical glass tube. The upper magnet hangs in the air above the lower one such that the distance between the nearest poles of the magnets is $3 \, mm$. The pole strength of each magnet is approximately ....... $A \cdot m$.

Some physical quantities are given in List-$I$ and their related units are given in List-$II$. Match the correct pairs.

List-$I$	List-$II$
$(A)$ Magnetic field intensity	$(i)$ $Wb$
$(B)$ Magnetic flux	(ii) $Wb \cdot m^{-2}$
$(C)$ Magnetic pole strength	(iii) $A \cdot m$
$(D)$ Magnetic induction	(iv) $A \cdot m^{-1}$