Derivation of Ampere's Law From Gauss's Law

Relation Between Gauss’s Law and Ampere’s Law

We know that Gauss’s Law

(Ñ.E)  = r    

Multiplying by velocity on both sides

(Ñ.E)v  = rv    

But rv = J   and J = (Ñ´ B) - ¶E/¶t (Ampere’s Law)

(Ñ.E)v  = (Ñ´ B) - ¶E/¶t

J  = (Ñ´ B) - ¶E/¶t

This implies that Ampere’s law is the relativistic consequence of Gauss’s Law

REFERENCE:

[1]. Naveed Hussain (2016),” Completely Generally Covariant Laws of Physics” Submitted to Frontiers of Physics, China, January 08 ,2016, Manuscript ID: FOP-2016- 0008