![]() ![]() ![]() These complex amplitude vectors are not functions of time, as they are understood to refer to oscillations over all time. 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. 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 electric field is the gradient of the potential. The electric field E can exert a force on an electric charge at any point in space. The above form for the Poynting vector represents the instantaneous power flow due to instantaneous electric and magnetic fields. Covariant formulation Scientists v t e In electromagnetism, electric flux is the measure of the electric field through a given surface, 1 although an electric field in itself cannot flow. 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. From this point of view D is frequently called the electric flux density, or free charge surface density, because of the close relationship between electric flux and electric charge. ![]() : 132 Nikolay Umov is also credited with formulating the concept. The value of the electric displacement D may be thought of as equal to the amount of free charge on one plate divided by the area of the plate. 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. ![]()
0 Comments
Leave a Reply. |