New Electromagnetic Fields and New Gravitational Fields--- Both with Sources Moving at Either Uniform Velocity, or Constant Acceleration, or Continuous Spin
In this article, we show that the vector calculus identities are powerful tool in both rederiving the
existing physical laws, such as Maxwell equations, and discovering new physical laws. First, we show
that the following physical laws can be rederived 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, and 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 magsnetic field. To rederive the above physical laws (1) to (8) shows 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: (1) for electric charges moving with either uniform
velocity v, or constant acceleration a, or continuous spin S; (2) for gravitational charges (mass) moving
with either uniform velocity v, or constant acceleration a, or continuous spin S. Electromagnetics and
gravitoelectromagnetics are derived from the vector calculus identities and have the same form, and
thus can be unified. The new physical field equations need to be tested experimentally.
