information:classification, stylistic:tone
Particle in a field

In Maxwell's equations, the forces between particles are mediated by electric and magnetic fields. The electromagnetic force (Lorentz force) on a particle with charge q due to a combination of electric field E and magnetic field B is

F = q (E + v × B). {\displaystyle \mathbf {F} =q(\mathbf {E} +\mathbf {v} \times \mathbf {B}).}

(in SI units). It has an electric potential φ (r, t) and magnetic vector potential A (r, t). In the non-relativistic regime, its generalized momentum is

P = m v + q A, {\displaystyle \mathbf {P} =m\mathbf {\mathbf {v} } +q\mathbf {A},}

while in relativistic mechanics this becomes

P = γ m v + q A. {\displaystyle \mathbf {P} =\gamma m\mathbf {\mathbf {v} } +q\mathbf {A}.}

The quantity V = q A is sometimes called the potential momentum. It is the momentum due to the interaction of the particle with the electromagnetic fields. The name is an analogy with the potential energy U = q φ, which is the energy due to the interaction of the particle with the electromagnetic fields. These quantities form a four-vector, so the analogy is consistent; besides, the concept of potential momentum is important in explaining the so-called hidden momentum of the electromagnetic fields.