$A$ magnet of magnetic moment $M$ and pole strength $m$ is divided into two equal parts. The magnetic moment of each part will be:

Assertion: The poles of a magnet cannot be separated by breaking it into two pieces.
Reason: The magnetic moment will be reduced to half when a magnet is broken into two equal pieces.

Use:
$(i)$ the Ampere's law for $\vec{H}$ and
$(ii)$ continuity of lines of $\vec{B}$,to conclude that inside a bar magnet,
$(a)$ lines of $\vec{H}$ run from the $N$ pole to $S$ pole,while
$(b)$ lines of $\vec{B}$ must run from the $S$ pole to $N$ pole.

Each atom of an iron bar $(5 \, cm \times 1 \, cm \times 1 \, cm)$ has a magnetic moment of $1.8 \times 10^{-23} \, A \cdot m^2$. Given that the density of iron is $7.78 \times 10^3 \, kg/m^3$,the atomic weight is $56 \, g/mol$,and Avogadro's number is $6.02 \times 10^{23} \, mol^{-1}$,calculate the magnetic moment of the bar in the state of magnetic saturation in $A \cdot m^2$.

$A$ steel wire has a magnetic moment $M$. What will be its magnetic moment if it is bent into a semi-circular arc?

Two magnetic poles have a pole strength of $0.01 \, A \cdot m$ each and are separated by a distance of $0.1 \, m$. What is the magnetic field at the midpoint between the two poles?