Compass and the Earth's field

Problem

Explain briefly why a compass aligns itself along the Earth’s field, and why at the magnetic North Pole a dip compass points downwards.

Solution

A compass needle is a small magnetic dipole, with magnetic moment $\vec\mu$. Immersed in the Earth’s field it experiences a torque $\vec M = \vec\mu\times\vec B$ that tends to align it with $\vec B$, bringing it to the minimum-energy configuration $U = -\vec\mu\cdot\vec B$. This is why the needle lines up along the direction of the field.

The Earth’s field is not horizontal everywhere: it has a vertical component that grows as one approaches the magnetic poles. At the magnetic North Pole the field lines enter the ground almost vertically; a dip compass, free to rotate in the vertical plane, aligns itself with these lines and so points DOWNWARDS. $\ev{\text{torque aligns the needle with } \vec B;\ \text{at the poles } \vec B \text{ is vertical}}$

Links

Topics: Magnetismo Concepts: Campo magnetico