The Lagrangian for a charged particle of mass m and charge q in an electromagnetic field equivalently describes the dynamics of the particle in terms of its energy, rather than the force exerted on it. The classical expression is given by: L = m 2 r ˙ ˙ ⋅ ⋅ r ˙ ˙ + q A ⋅ ⋅ r ˙ ˙ − − q ϕ ϕ where A and ϕ are the potential fields as above. The quantity V = q ( ϕ ϕ − − A ⋅ ⋅ r ˙ ˙ ) can be thought as a velocity-dependent potential function. Using Lagrange's equations, the equation for the Lorentz force given above can be obtained again.