Maxwell Equations Derived from Coulomb' Law Mathematically vs

A Universal Mathematical Field Theory (UMFT) is established and states
that the combination of the operations of both gradient and divergence
of vector fields, such as electric field and velocity field, create the
curl of an axial vector field, such as magnetic field. Utilizing UMFT,
Extended-Maxwell equations and the equation of Lorentz force are derived
from the combination of Coulomb’s law and velocity of source
mathematically, and new effects are predicted. For uniformly moving
source, Extended-Maxwell equations reduce to Maxwell equations. This
derivation mathematically explains how a moving electric charge creates
magnetic field, and shows that there is no magnetic monopole charge. The
duality between the Newton’s law and the Coulomb’s law leads us to
derive Maxwell-type gravitational equations and Lorentz-type
gravitational force by combining UMFT, the Newton’s law and velocity of
gravitational source, denoted as Gravito-electromagnetic, which is dual
of Electromagnetics. The benefits of the duality are that the effects
and phenomena of Electromagnetics may be directly converted to that of
gravity. The Gravito-Electromagnetics are employed to study the
accelerating expansion of the universe, rotation curve, virial theorem,
and gravitation radiation.