Appendix J
Gaussian, S.I., and Atomic Units
J.1 Maxwell’s Equations in Gaussian Units
When dealing with systems of particles that interact with electro-magnetic fields,
Gaussian units are often the most convenient units to use because all electric and
magnetic quantities are expressed in terms the mechanical units of grams (g),
centimeters (cm), seconds (s).
In Gaussian (cgs) units, Maxwell’s equations in a vacuum are (Jackson 1975)
Gauss’s laws :
∇·E = 4πρ, ∇·B = 0
Ampere’s law :
∇×B −
1
c
∂E
∂t
=
4π
c
J Q ,
Faraday’s law :
∇×E +
1
c
∂B
∂t
= 0
Lorentz force;
F = Q
E +
v
c
×B
(J.1)
where E is the electric field, B is the magnetic field, c is the speed of light, Q is the
electric charge, and J Q is the charge current. The force between two charges, Q 1
and Q 2 , a distance r apart, is is
F =
Q 1 Q 2
r 2 .
The potential energy between for a particle with magnetic moment μ in the presence
of a magnetic field is
U = −μ·B.
© Springer Nature Switzerland AG 2021
L. Reichl, The Transition to Chaos, Fundamental Theories of Physics 200,
https://doi.org/10.1007/978-3-030-63534-3
525