Mathematics Equations to Physics Field Equations --- Sources Moving with Velocity, Acceleration, and Spin

Author(s)

Abstract
In this article, we show that mathematics can be applied to discover physical laws. First, we show that the following physical laws can be derived from the vector calculus identities: (1) Poynting's Theorem; (2) Gauss's Law for Magnetism; (3) Charge density Continuity equation; (4) Wave equation of potential A/electric field E/magnetic field B; (5) Faraday's Law of Induction; (6) energy density of the magnetic field; (7) time change of energy density of the electric field; (8) time change of energy density of the magnetic field. The above way to rederive physical laws (1) to (8) show the validation and power of the vector calculus identities in discovering physical laws. Then, applying the vector calculus identities, we derive NEW physical field equations for electric charges moving with either uniform velocity v, or constant acceleration a, or continuous spin S. The new physical laws need to be tested experimentally. We suggest that AI can follow the above approach, Mathematical equation → physics theory, to discover new physics laws.

Keywords
vector calculus identities, field equation, electric field, magnetic field, spin

Cite this paper
Hui Peng, Mathematics Equations to Physics Field Equations --- Sources Moving with Velocity, Acceleration, and Spin , SCIREA Journal of Physics. Volume 11, Issue 4, August 2026 | PP. 169-191. 10.54647/physics140727

References