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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.
In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem , and it relates the distribution of electric charge to the resulting electric field .
The divergence theorem is employed in any conservation law which states that the total volume of all sinks and sources, that is the volume integral of the divergence, is equal to the net flow across the volume's boundary. [3]
In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics. It states that the magnetic field B has divergence equal to zero, [ 1 ] in other words, that it is a solenoidal vector field .
Mathematically, we can state the law of charge conservation as a continuity equation: = ˙ ˙ (). where / is the electric charge accumulation rate in a specific volume at time t, ˙ is the amount of charge flowing into the volume and ˙ is the amount of charge flowing out of the volume; both amounts are regarded as generic functions of time.
In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.
Electromagnetic radiation; Faraday law; ... is that the Lorentz invariant divergence of J is ... is defined as the divergence of the electromagnetic ...
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.