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A Field Equation is an equation in a Physical Theory that describes how a Fundamental Force (or a combination of such forces) interacts with Matter . The four fundamental forces are the Gravitational Force , the Electromagnetic Force , the Strong Nuclear Force and the Weak Nuclear Force . Before the theory of Quantum Mechanics was fully developed, there were two known field theories, namely Gravitation and Electromagnetism (these two are sometimes referred to as Classical Field Theories , as they were formulated before the advent of quantum mechanics, and hence do not take into account quantum phenomena). Modern field equations tend to be Tensor Equation s. NEWTON'S THEORY OF UNIVERSAL GRAVITATION The first Field Theory of gravity was Newton's Theory Of Gravitation , which described gravity as obeying an inverse square law. This was very useful in describing the motion of planets around the Sun. LAPLACE'S EQUATION Newton's theory involved two-body motion and gravity. However, there are more than two massive objects in the solar system, therefore, each planet contributes to perturbations of the orbits of the other planets with Jupiter making the largest contribution. French mathematician Pierre Simon De Laplace created an equation that tried to solve the problem of the Solar System's stability by making some simplifying assumptions about the nature of the gravitational interactions of the planets. POISSON'S EQUATION The term "potential theory" arises from the fact that, in 19th century physics, the fundamental forces of nature were believed to be derived from potentials which satisfied Laplace's equation. Poisson addressed the question of the stability of the planetary orbits, which had already been settled by Lagrange to the first degree of approximation for the disturbing forces and created Poisson's Equation . EINSTEIN'S FIELD EQUATION See Also: Einstein field equation Newtonian Gravitation is now superseded by Einstein's theory of General Relativity , in which Gravitation is thought of as being due to a curved Spacetime , caused by masses. The Einstein field equation - which describes how this curvature is produced by masses - is: MAXWELL'S EQUATIONS See Also: Maxwell's equations The electromagnetic force is best described by Maxwell's Theory Of Electromagnetism . The field equations of Classical Electromagnetism are Maxwell's equations which describe how electromagnetic fields are produced from charged particles and are written in the framework of Special Relativity (which was devised to consistently describe electromagnetism and Classical Mechanics ) as: KALUZA-KLEIN FIELD EQUATIONS See Also: Kaluza-Klein theory VACUUM FIELD EQUATIONS ''Vacuum field equations'' are the field equations written without matter (including sources). Solutions of the vacuum field equations are called Vacuum Solution s. SEE ALSO REFERENCES
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