A compass needle free to turn in a horizontal plane is placed at the centre of a circular coil of $30$ turns and radius $12 \mathrm{cm}$. The coil is in a vertical plane making an angle of $45°$ with the magnetic meridian. When the current in the coil is $0.35 \mathrm{A}$, the needle points west to east.
The current in the coil is reversed and the coil is rotated about its vertical axis by an angle of $90°$ in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.

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 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 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.)

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 $I.$