![]() Each of these forms in turn can also be expressed two ways: In terms of a relation between the electric field E and the total electric charge, or in terms of the electric displacement field D and the free electric charge. The law can be expressed mathematically using vector calculus in integral form and differential form, both are equivalent since they are related by the divergence theorem, also called Gauss’s theorem. In words, Gauss’s law states that: The net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed within that closed surface. In fact, Gauss’s law does hold for moving charges, and in this respect Gauss’s law is more general than Coulomb’s law. Note that since Coulomb’s law only applies to stationary charges, there is no reason to expect Gauss’s law to hold for moving charges based on this derivation alone. ![]() Gauss’s law can be used to derive Coulomb’s law, and vice versa. It is one of the four Maxwell’s equations which form the basis of classical electrodynamics, the other three being Gauss’s law for magnetism, Faraday’s law of induction, and Ampère’s law with Maxwell’s correction.Ĭarl Friedrich Gauss: Carl Friedrich Gauss (1777–1855), painted by Christian Albrecht Jensen The law was formulated by Carl Friedrich Gauss (see ) in 1835, but was not published until 1867. Gauss’s law, also known as Gauss’s flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Describe relationship between the Gauss’s law and the Coulomb’s law.Thus, the SI base units of electric flux are kg Examples include spherical and cylindrical symmetry.Įlectric flux has SI units of volt metres (V m), or, equivalently, newton metres squared per coulomb (N m 2 C −1). While Gauss’ Law holds for all situations, it is only useful for “by hand” calculations when high degrees of symmetry exist in the electric field. It is important to note that while the electric flux is not affected by charges that are not within the closed surface, the net electric field, E, in the Gauss’ Law equation, can be affected by charges that lie outside the closed surface. We would thus not be considering the instantaneous E( t) and H( t) used above, but rather a complex (vector) amplitude for each which describes a coherent wave's phase (as well as amplitude) using phasor notation.\) where E is the electric field and dS is a differential area on the closed surface S with an outward facing surface normal defining its direction. The results can then be applied more generally, for instance, by representing incoherent radiation as a superposition of such waves at different frequencies and with fluctuating amplitudes. ![]() More commonly, problems in electromagnetics are solved in terms of sinusoidally varying fields at a specified frequency. The above form for the Poynting vector represents the instantaneous power flow due to instantaneous electric and magnetic fields. The Poynting vector and theorem and expression for energy density are universally valid in vacuum and all materials. Since only the microscopic fields E and B occur in the derivation of S = (1/ μ 0) E × B and the energy density, assumptions about any material present are avoided. In all other cases, they differ in that S = (1/ μ 0) E × B and the corresponding u are purely radiative, since the dissipation term − J ⋅ E covers the total current, while the E × H definition has contributions from bound currents which are then excluded from the dissipation term. The two alternative definitions of the Poynting vector are equal in vacuum or in non-magnetic materials, where B = μ 0 H. It can be derived directly from Maxwell's equations in terms of total charge and current and the Lorentz force law only. In Poynting's original paper and in most textbooks, the Poynting vector S The Poynting vector is used throughout electromagnetics in conjunction with Poynting's theorem, the continuity equation expressing conservation of electromagnetic energy, to calculate the power flow in electromagnetic fields. Oliver Heaviside also discovered it independently in the more general form that recognises the freedom of adding the curl of an arbitrary vector field to the definition. : 132 Nikolay Umov is also credited with formulating the concept. It is named after its discoverer John Henry Poynting who first derived it in 1884. The SI unit of the Poynting vector is the watt per square metre (W/m 2) kg/s 3 in base SI units. In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or power flow of an electromagnetic field.
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