The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $150 \mathrm{ms}$. The magnet is cut perpendicular to its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination (in $\mathrm{ms}$) 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 coil of $50$ turns carrying a current of $2\mathrm{A}$ in a magnetic field of $0.5\mathrm{T}$. The torque acting on the coil 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______.

The rectangular coil of area $A$ is in a field $B.$ Find the torque about the $Z$-axis when the coil lies in the position shown and carries a current $I.$

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.)

Two short magnetic dipoles $m_1$ and $m_2$ each having magnetic moment of $1 \mathrm{A} {\mathrm{m}}^2$ are placed at point $O$ and $P$ respectively. The distance between $OP$ is $1 \mathrm{m}$. The torque experienced by the magnetic dipole $m_2$ due to the presence of $m_1$ is $\_\_\_\_\_\_\_\_\times {10}^{-7}\mathrm{N} \mathrm{m}$.

A magnetic dipole is oscillating in a magnetic field obeying the following expression

$\frac{{\mathrm{d}}^2\mathrm{\theta }}{{\mathrm{dt}}^2}=-\frac{\mathrm{mB}}{\mathrm{I}}\mathrm{\theta }$:

What is the time period of oscillation and mention the nature of oscillation?

A $100$ turns coil shown in figure carries a current of $2 \mathrm{A}$ in a magnetic field $B=0.2 \mathrm{Wb} {\mathrm{m}}^{-2}.$ The torque acting on the coil is