A Theoretical Derivation of Faraday's Second Law of Electromagnetic Induction

Fraday's law of induction is one of the most important laws in electromagnetism. In this paper, based on the curl of electric field vector generated from a moving charge, we show a detailed derivation process, which describes how to derive the rate of change of the magnetic field with time from the curl of the electric field vector. From the mathematical derivation, we found that the acceleration of the charge movement can generate one electric field, which is essentially equivalent to the a non-conservative electric field excited by the ratio of change of magnetic field with time. The theoretical derivation is meaningful to explore the nature of electromagnetic field transformation.