Maxwell Equations Derived from Coulomb’ Law Mathematically vs. Maxwell-type Gravity Derived from Newton’s Law Mathematically

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.