Abstract
Taylor's formula is an important content in advanced mathematics, and it is also an indispensable mathematical tool in the study of function limits and error estimation. In this paper, Taylor's formula is used to deduce the electric potential energy of the charge system in the applied electric field and to prove the Noether's theorem of the point particle system under the action of conservative force. Finally, the expression of potential energy of multi electrode in external electric field and the reason why Noether's theorem is established in conservative system are given, and the superposition principle of potential energy of point particle system is indirectly explained.
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