The magnetic potential at a point on the axial line of a bar magnet of dipole moment $M$ is $V$. What is the magnetic potential due to a bar magnet of dipole moment $\frac{M}{4}$ at the same point

Verify the Ampere’s law for magnetic field of a point dipole of dipole moment ${\rm{\vec M = M\hat k}}$. Take $\mathrm{C}$ as the closed curve running clockwise along : the $\mathrm{z}$ - axis from $\mathrm{z} = \mathrm{a} \,>\, 0$ to $\mathrm{z = R}$;

A bar magnet of magnetic moment $M$ is placed at right angles to a magnetic induction $B.$ If a force $F$ is experienced by each pole of the magnet, the length of the magnet will be

A magnetic needle of negligible breadth and thickness compared to its length, oscillates in a horizontal plane with a period $T$. The period of oscillation of each part obtained on breaking the magnet into $n$ equal parts perpendicular to the length is

The direction of line of magnetic field of bar magnet is

Two bar magnets with magnetic moments $ 2 M $ and $M$ are fastened together at right angles to each other at their centres to form a crossed system, which can rotate freely about a vertical axis through the centre. The crossed system sets in earth’s magnetic field with magnet having magnetic moment $2M $ making and angle  $ \theta $ with the magnetic meridian such that