$A$ magnetized wire of magnetic moment $M$ and length $L$ is bent into an arc of a circle subtending an angle of $60^{\circ}$ at the center. The new magnetic moment is:

$A$ magnet is placed in iron powder and then taken out,then maximum iron powder is at

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 $z$-axis from $z = a > 0$ to $z = R$,then along the circular arc of radius $R$ to the $x$-axis,then along the $x$-axis to $x = a$,and finally along the circular arc of radius $a$ back to the $z$-axis.

The intensity of magnetization of a bar magnet is $5.0 \times 10^{4} \text{ A m}^{-1}$. The magnetic length and the area of cross-section of the magnet are $12 \text{ cm}$ and $1 \text{ cm}^{2}$ respectively. The magnitude of the magnetic moment of this bar magnet is (in $SI$ unit):

The following figures show the arrangement of bar magnets in different configurations. Each magnet has a magnetic dipole moment $\vec{m}$. Which configuration has the highest net magnetic dipole moment?

$A$ wire of magnetic material of length $2L$ and magnetic moment $M$ is bent at the centre to form an $L$-shaped wire. Its magnetic moment is