# Classical mechanics methods application to electric charges

DOI: 10.34759/trd-2021-119-01

### Аuthors

Popov I. P.

Kurgan State University, 63/4, Sovetskaya str., Kurgan, 640020, Russia

e-mail: ip.popow@yandex.ru

### Abstract

The article proves three theorems associated with studying accelerated electric charges on the basis and in terms of classical mechanics. Active development of aerospace ion and plasma engines theory touches upon a number of aspects, the two of which are being considered in the presented work, namely the charged particles dynamics and electromagnetic radiation at their acceleration. It is assumed that the charge moving along the circular path, i.e. with the centripetal acceleration, should necessarily radiate electromagnetic waves. It spreads, inter alia, to the cyclotron radiation.

The terms and methods of classical mechanics are being used, which spread, inter alia, to the electric charges dynamics in a part of forces, accelerations, displacements, work and energy. The starting point is a credible statement. A number of mathematically correct transformations is being performed with it. Thus, the result is necessarily reliable. Electromagnetic waves possess momentum and energy. The wave receives energy from the energy source, which leads to energy reduction of the source itself. At the same time, any decrease in energy is being necessarily stipulated by the corresponding work performing. Three theorems has been proved. Theorem 1. A tangentially accelerated charge does emit electromagnetic waves. Theorem 2. A normally accelerated charge does not emit electromagnetic waves. Theorem 2 formalizes a well-known in mechanics circumstance that the centripetal force does not perform work (since the scalar product of orthogonal vectors must be zero). Theorem 3. Electric charge satisfies Newton’s second law. In view of Theorems 1 and 2, the cause of magnetron radiation should be sought in the tangential acceleration caused by the Coulomb interactions of the beam charges.

### Keywords:

electromagnetic waves, dot product, orthogonal vectors, inactivity

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