Lorentz Force in Terms of Potentials
See also: Mathematical descriptions of the electromagnetic field, Maxwell's equations, and Helmholtz decompositionThe 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:
“what affects our hearts
Is not the exactness of peculiar parts;
Tis not a lip, or eye, we beauty call,
But the joint force and full result of all.”
—Alexander Pope (16881744)
“One of your biggest jobs as a parent of multiples is no bigger than simply talking to your children individually and requiring that they respond to you individually as well. The benefits of this kind of communication can be enormous, in terms of the relationship you develop with each child, in terms of their language development, and eventually in terms of their sense of individuality, too.”
—Pamela Patrick Novotny (20th century)