Editing Classical electromagnetism (section)

== Lorentz force ==
{{Main|Lorentz force}}

The electromagnetic field exerts the following force (often called the Lorentz force) on [[Electric charge|charged]] particles:

:<math>
\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})
</math>

where all boldfaced quantities are [[Vector (geometric)|vectors]]: {{math|'''F'''}} is the force that a particle with charge ''q'' experiences, {{math|'''E'''}} is the [[electric field]] at the location of the particle, {{math|'''v'''}} is the velocity of the particle, {{math|'''B'''}} is the [[magnetic field]] at the location of the particle.

The above equation illustrates that the Lorentz force is the sum of two vectors. One is the [[cross product]] of the velocity and magnetic field vectors. Based on the properties of the cross product, this produces a vector that is perpendicular to both the velocity and magnetic field vectors. The other vector is in the same direction as the electric field. The sum of these two vectors is the Lorentz force.

Although the equation appears to suggest that the electric and magnetic fields are independent, the equation [[Covariant formulation of classical electromagnetism#Lorentz force|can be rewritten]] in term of [[four-current]] (instead of charge) and a single [[electromagnetic tensor]] that represents the combined field (<math>F^{\mu \nu}</math>):
:<math>f_{\alpha} = F_{\alpha\beta}J^{\beta} .\!</math>