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These equations are inhomogeneous versions of the wave equation, with the terms on the right side of the equation serving as the source functions for the wave. As with any wave equation, these equations lead to two types of solution: advanced potentials (which are related to the configuration of the sources at future points in time), and ...
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Formula Sheet Equation Editor [permanent dead link ] Yes Yes No Yes Yes Yes No No Online LaTeX equation editor with real-time .png, .pdf, and .tex output. Customizable resolution, font, and color. One click copy to MS Word 2007+ using MathML. Formulator MathML Weaver: Yes Yes No No Yes Yes No No Dual-licensing (Open source and commercial).
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.
The templates {} and {{EquationRef}} can be used to number equations. The template {{EquationNote}} can be used to refer to a numbered equation from surrounding text. For example, the following syntax: {{NumBlk |: |< math > x ^ 2 + y ^ 2 + z ^ 2 = 1 </ math >|{{EquationRef | 1}}}} produces the following result (note the equation number in the ...
A word equation is a formal equality:= = between a pair of words and , each over an alphabet comprising both constants (c.f. ) and unknowns (c.f. ). [1] An assignment of constant words to the unknowns of is said to solve if it maps both sides of to identical words.
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The matrix form of the Maxwell's equations is used as a candidate for the Photon Wavefunction. [8] Historically, the geometrical optics is based on the Fermat's principle of least time. Geometrical optics can be completely derived from the Maxwell's equations. This is traditionally done using the Helmholtz equation.