Search results
Results From The WOW.Com Content Network
where: is the rate of change of the energy density in the volume. ∇•S is the energy flow out of the volume, given by the divergence of the Poynting vector S. J•E is the rate at which the fields do work on charges in the volume (J is the current density corresponding to the motion of charge, E is the electric field, and • is the dot product).
More rigorously, it is the quantity that must be used to make Poynting's theorem valid. Poynting's theorem essentially says that the difference between the electromagnetic energy entering a region and the electromagnetic energy leaving a region must equal the energy converted or dissipated in that region, that is, turned into a different form ...
All but the last term of can be written as the tensor divergence of the Maxwell stress tensor, giving: = +, As in the Poynting's theorem, the second term on the right side of the above equation can be interpreted as the time derivative of the EM field's momentum density, while the first term is the time derivative of the momentum density for ...
For the special case of = , this gives a re-statement of conservation of energy or Poynting's theorem (since here we have assumed lossless materials, unlike above): The time-average rate of work done by the current (given by the real part of ) is equal to the time-average outward flux of power (the integral of the Poynting vector). By the same ...
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. These ...
The equations take this form with the International System of Quantities. When dealing with only nondispersive isotropic linear materials, Maxwell's equations are often modified to ignore bound charges by replacing the permeability and permittivity of free space with the permeability and permittivity of the linear material in question.
Poynting may refer to: John Henry Poynting (1852–1914), a British physicist, after whom are named: Poynting vector, a representation of the energy flux of an electromagnetic field; Poynting's theorem on conservation of energy in electromagnetic field; Poynting (lunar crater), crater on the Moon; Poynting (Martian crater), crater on Mars
the mass–energy equivalence formula which gives the energy in terms of the momentum and the rest mass of a particle. The equation for the mass shell is also often written in terms of the four-momentum ; in Einstein notation with metric signature (+,−,−,−) and units where the speed of light c = 1 {\displaystyle c=1} , as p μ p μ ≡ p ...