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

Read more about this topic:  Lorentz Force

Famous quotes containing the words force and/or terms:

    “Then for the Style; Majestick and Divine,
    It speaks no less than God in every Line:
    Commanding words; whose Force is still the same
    As the first Fiat that produc’d our Frame.”
    —John Dryden (1631–1700)

    “I hope that you live on good terms with yourself and the gods.”
    —Henry David Thoreau (1817–1862)