Abstract:
The momentum change law for the electromagnetic field is derived and formulated in a tensor, that is, in covariant form. Covariant analysis allows us to explore a wide range of problems that are difficult or impossible to consider with the traditional approach, for example, to investigate a momentum change in non-inertial reference frames or in curved coordinates. The standard Lagrangian of the electromagnetic field is used in the derivation. It is demonstrated that the use of the standard Lagrangian in the formulation of the law of momentum change leads to the fact that a change in the momentum of the field is equal to a change in the momentum of the charged medium that creates the field, with the opposite sign. As an illustrative example, a charge oscillating according to the harmonic law is considered. The energy transferred by the charge to the field is found. It is equal to the energy carried away by the field, as follows from the calculation. This approach can also be used to analyze the conservation and change of the momentum in the emission of gravitational waves.
Keywords:covariant analysis, Lagrangian variation, momentum change law for the electromagnetic field, oscillating charge radiation.
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