Competitive Thinking

At a place on the Earth, the vertical component of Earth's magnetic field is $\sqrt{3}$ times its horizontal component. The angle of dip at this place is

The ratio of magnetic fields due to a bar magnet at the two axial points $P_1$ and $P_2$ which are separated from each other by $10 \mathrm{cm}$ is $25:2$. Point $P_1$ is situated at $10 \mathrm{cm}$ from the centre of the magnet. Magnetic length of the bar magnet is (Points $P_1$ and $P_2$ are on the same side of magnet and distance of $P_2$ from the centre is greater than distance of $P_1$ from the centre of magnet)

Which magnetic field is similar to that of a bar magnet?

A circular loop and a square loop are formed from two wires of the same length and cross-section. The same current is passed through them. Then the ratio of their dipole moments is

A charge $q$ is spread uniformly over an isolated ring of radius $R$. The ring is rotated about its natural axis with an angular velocity $\omega$. The magnetic dipole moment of the ring is

At neutral point, the horizontal component of the magnetic field due to a magnet is

Assertion: If a compass needle be kept at magnetic north pole of the earth, the compass needle may stay in any direction.

Reason: Dip needle will stay vertical at the north pole of earth.

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by $60°$ is $\mathrm{W}.$ Now the torque required to keep the magnet in this new position is