The magnetic lines of force inside a bar magnet

What is the magnitude of the equatorial and axial fields due to a bar magnet of length $5.0 \; cm$ at a distance of $50 \; cm$ from its mid-point? The magnetic moment of the bar magnet is $0.40 \; A m^{2}$.

$A$ short bar magnet has a length $2l$ and a magnetic moment $10 \text{ Am}^2$. Find the magnetic field at a distance of $z = 0.1 \text{ m}$ from its centre on the axial line. Here,$l$ is negligible as compared to $z$.

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 $A \cdot m^2$.

The force between two identical bar magnets whose centres are $r \ m$ apart is $4.8 \ N$,when their axes are in the same line. If the separation is increased to $2r$,the force between them is reduced to . . . . . . $N$.

$A$ long magnetic needle of length $2L$,magnetic moment $M$,and pole strength $m$ is broken into two equal pieces at the middle. The magnetic moment and pole strength of each piece will be