A magnetic field is a vector field that describes magnetic influence throughout space. It is written $\mathbf B$ and measured in teslas ($\mathrm T$).

Direction

At each point, $\mathbf B$ has a direction and magnitude. Magnetic-field lines are drawn tangent to the field and form continuous loops rather than beginning or ending on isolated magnetic charges.

Sources

Magnetic fields are produced by moving electric charges, electric currents and magnetic materials. Later laws describe these sources quantitatively.

Field versus force

A magnetic field is not itself a force. The force it exerts depends on what is placed in the field and on that object's motion or magnetic properties.

For a moving charged particle, the magnetic part of the Lorentz force is perpendicular to both the particle velocity and the magnetic field.

Superposition

Magnetic fields add vectorially:

$$\mathbf B_{\mathrm{total}}=\sum_i\mathbf B_i.$$

The field concept lets different magnetic sources be combined before asking how a particular charge, wire or material responds.