The time period of a freely suspended magnet is $4 \ s$. If it is broken in length into two equal parts and one part is suspended in the same way,then its time period will be: (in $s$)

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 $A \cdot m^2$.

$A$ magnetic rod of length $L$ has a magnetic dipole moment $M$. If it is bent into a semicircle,what will be its new magnetic dipole moment?

$A$ bar magnet with a magnetic moment of $3.0 \, A \cdot m^2$ is placed in a magnetic field of $2 \times 10^{-5} \, T$. If the force acting on each pole is $6 \times 10^{-4} \, N$,what is the length of the magnet in $m$?

The magnetic moment of a magnet of length $10\, cm$ and pole strength $4.0\, Am$ will be......$A\,m^2$.

Verify Ampere's law for the magnetic field of a point dipole with dipole moment $\vec{M} = M\hat{k}$. Take $C$ as the closed curve running clockwise along the $x$-axis from $x = R$ to $x = a$,then along a circular arc of radius $r$ in the $xz$-plane from $\theta = 0$ to $\theta = \pi$,and finally back to the starting point.