Lorentz Force - Lorentz Force in Terms of Potentials

Lorentz Force in Terms of Potentials

See also: Mathematical descriptions of the electromagnetic field, Maxwell's equations, and Helmholtz decomposition

The E and B fields can be replaced by the magnetic vector potential A and (scalar) electrostatic potential ϕ by

where ∇ is the gradient, ∇• is the divergence, ∇ × is the curl.

The force becomes

and using an identity for the triple product simplifies to

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