The Classical Electromagnetic Field by Eyges Leonard;

Author:Eyges, Leonard; [Eyges, Leonard]
Language: eng
Format: epub, azw3
ISBN: 1909562
Publisher: Dover Publications
Published: 2012-10-11T16:00:00+00:00

(11.69)

Now ∫wm dυ is the kinetic energy of the particles, so we can write this equation as

(11.70)

As we have seen in electrostatics, the integral (1/8π) ∫ |E|2 dυ can also be written as j<i i (qiqj/r¡j), the sum of the mutual Coulomb potential energies of the particles. So we find that Eq. (11.70) is simply the ordinary energy conservation law stating that the sum of the kinetic and potential energies of the charges plus the magnetic field energy (the energy of assemblage of the currents) is constant.

In the case of the momentum conservation theorem, we take the volume V0 to be the same as that for the energy theorem and again argue that the surface integral vanishes so that (11.64) becomes

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