A magnetic field is a region in space where a magnetic force can act on moving electric charges or magnetic dipoles. It is represented mathematically by the vector field \$\mathbf{B}\$, where each point in space has a direction and a magnitude. Think of it as an invisible “force map” that tells a moving charge how to turn.
The field is produced by:
Mathematically, the magnetic field satisfies two key equations:
\$\nabla \cdot \mathbf{B} = 0\$
and
\$\nabla \times \mathbf{B} = \mu0 \mathbf{J} + \mu0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}.\$
The first equation tells us that magnetic field lines never start or end – they form closed loops. The second relates the field to currents \$\mathbf{J}\$ and changing electric fields \$\mathbf{E}\$.
Field lines are a handy way to picture a magnetic field. They follow these rules:
Imagine a bar magnet 🧲. If you sprinkle iron filings around it, the filings line up along invisible paths – those are the field lines. The filings show that the field is strongest near the poles and weaker in the middle.
| Property | Description |
|---|---|
| Direction | Points from north to south outside the magnet; inside the magnet, from south to north. |
| Density | Higher density = stronger field. |
| Continuity | Field lines never begin or end; they form closed loops. |
| Interaction with Charges | A moving charge experiences a force \$\mathbf{F} = q \mathbf{v} \times \mathbf{B}\$, perpendicular to both velocity and field. |
This simple experiment shows that magnetic fields are real, even though we can’t see them directly. They guide the filings, just as they guide moving charges in circuits and motors.