The work done in rotating a bar magnet of magnetic moment $\mathrm{M}$ from its unstable equilibrium position to its stable equilibrium position in a uniform magnetic field is $\mathrm{B}$is

A bar magnet is oscillating in Earth's magnetic field with the time period $\mathrm{T}$. If a similar magnet with the same mass and dimensions has magnetic dipole moment $4$ times that of this magnet, then the periodic time will be______.

A square loop of dimensions $0.4 \mathrm{m}\times 0.3 \mathrm{m}$ consists of $100$ closely wrapped turns. The loop is hinged along the $y$-axis. A uniform magnetic field of $0.75 \mathrm{T}$ is directed along the $x$-axis.

How much current should flow in the loop so that the maximum torque exerted on the loop is $18 \mathrm{N}-\mathrm{m}?$

A short bar magnet is placed in the magnetic meridian of the earth with North Pole pointing north. Neutral points are found at a distance of $30 \mathrm{cm}$ from the magnet on the East-West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in ${\mathrm{Am}}^2$ is close to:

(Given $\frac{{\mu }_0}{4\pi }={10}^{-7}$ in SI units and $B_H=$ Horizontal component of earth's magnetic field $=3.6\times {10}^{-5}$ Tesla.)

A current carrying loop is placed in a uniform magnetic field in four different orientations I, II, III and IV as shown in figure. Arrange them in decreasing order of potential energy.