A short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 G experiences a torque of 0.016 Nm . The magnetic moment of the bar magnet is

A solenoid has a core of a material with relative permeability $\frac{800}{\pi}$. The windings of the solenoid are insulated from the core and carry current of 2 A . If the number of turns is 1000 per metre, find the magnetic field $B$.

Let $m$ and $r$ are the dipole moment and radius of earth respectively. Then, the earth's magnetic field at the equator is

Two short magnets of equal dipole moments $M$ are fastened perpendicularly at their centres which lies at origin. Let two magnets lie along $X$-axis and $Y$-axis, respectively.

The magnitude of the magnetic field at a distance $R$ from the centre on the $Y$-axis is $\frac{\mu_0}{4 \pi} \frac{M_0}{R^3}$. Assuming, $R \gg l$ (magnet length), the magnitude of $M$ is