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the closed surface S at the moment when its charge is evaluated, but since the charges on the particles are evaluated at different times, the particles need not all be within the closed surface at a given time. This explains why the total charge is not

$\int \int \int \rho \ dx\ dy\ dz$

The double integral expresses the total charge as a surface integral, but here again the particles over which the integration extends are not all on the surface at the same time, but at different times.

In the same way equation (II) may be regarded as a general way of expressing the fact that there is no free magnetism.

If Φ is the scalar electromagnetic potential and $\left(A_{x},A_{y},A_{z}\right)$ the components of the electromagnetic vector potential, we have

$E_{x}=-{\frac {\partial \Phi }{\partial x}}-{\frac {\partial A_{x}}{\partial t}},\ H_{x}={\frac {\partial A_{z}}{\partial y}}-{\frac {\partial A_{y}}{\partial z}}.$