ABSTRACT
A real physical meaning can only be devoted to the electric current density Je(R, t) defined as transport of electric charge; attributing an electric charge q to a specific particle density n(R, t) instead of a mass according to (3.25), we obtain the electric current density
e(R, t) = q n(R, t), (6.5)
K12611 Chapter: 6 page: 169 date: January 18, 2012
K12611 Chapter: 6 page: 170 date: January 18, 2012
and Je(R, t) is analogously to the mechanical momentum density (Equation 3.26) defined as the corresponding transport quantity
Je(R, t) = e(R, t)v(R, t). (6.6)
Accordingly, mass conservation (3.28) yields charge conservation
∇ · Je(R, t) + ∂e(R, t)
∂t = 0 (6.7)
in terms of a continuity equation (de Hoop 1995). If magnetic charges would physically exist, we could define the magnetic current density
Jm(R, t) = m(R, t)v(R, t) (6.8)
similarly to (6.6), and we would obtain the continuity equation
∇ · Jm(R, t) + ∂m(R, t)
∂t = 0. (6.9)
As a matter of fact, magnetic charge and current densities are only auxiliary quantities primarily resulting from symmetry considerations for Maxwell’s equations.
