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Maxwell's equations on a plaque on his statue in Edinburgh. Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits.
Mass–energy equivalence states that all objects having mass, or massive objects, have a corresponding intrinsic energy, even when they are stationary.In the rest frame of an object, where by definition it is motionless and so has no momentum, the mass and energy are equal or they differ only by a constant factor, the speed of light squared (c 2).
The Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor in three dimensions that is used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy ...
The way in which charges and currents (i.e. streams of charges) interact with the electromagnetic field is described by Maxwell's equations [4] and the Lorentz force law. [5] Maxwell's equations detail how the electric field converges towards or diverges away from electric charges, how the magnetic field curls around electrical currents, and ...
Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell .
Starting from the basic equation of general relativity, the Einstein field equation, and assuming a weak gravitational field or reasonably flat spacetime, the gravitational analogs to Maxwell's equations for electromagnetism, called the "GEM equations", can be derived. GEM equations compared to Maxwell's equations are: [11] [12]
The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields.
The generalized force, X, corresponding to the external parameter x is defined such that is the work performed by the system if x is increased by an amount dx. E.g., if x is the volume, then X is the pressure. The generalized force for a system known to be in energy eigenstate is given by: