Magnetic fields are the companion to electric fields — but they play by different rules.

How magnetic fields arise

Every magnetic field traces back to moving charges (electric current):

• A current-carrying wire is surrounded by a magnetic field that circles the wire
• An electron orbiting a nucleus creates a tiny magnetic field
• Even a spinning electron (its intrinsic “spin”) creates a magnetic field

The rule: currents create loops. The magnetic field wraps around the current in circles, described by the right-hand rule — point your thumb in the direction of current flow, and your fingers curl in the direction of $\mathbf{B}$.

No magnetic monopoles

Here’s the deepest difference between electric and magnetic fields:

• Electric fields have sources (positive charges) and sinks (negative charges)
• Magnetic field lines always form closed loops — they never start or end anywhere

You can have an isolated positive charge (a proton). You cannot have an isolated north pole. Cut a bar magnet in half and you get two smaller bar magnets, each with both a north and south pole.

This is why $\nabla \cdot \mathbf{B} = 0$ — the divergence of the magnetic field is always zero. No sources, no sinks, ever.

Electric vs magnetic: a comparison

The magnetic force is perpendicular to both the velocity and the field — it deflects moving charges without speeding them up or slowing them down.