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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 n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Gauss's law. Foundational law of electromagnetism relating electric field and charge distributions. Gauss's law in its integral form is particularly useful when, by symmetry reasons, a closed surface (GS) can be found along which the electric field is uniform. The electric flux is then a simple product of the surface area and the strength of ...
Jefimenko's equations (or the closely related Liénard–Wiechert potentials) are the explicit solution to Maxwell's equations for the electric and magnetic fields created by any given distribution of charges and currents. It assumes specific initial conditions to obtain the so-called "retarded solution", where the only fields present are the ...
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m −3), at any point in a volume. [1][2][3] Surface charge density (σ) is ...
Electromagnetism. In electromagnetism, Jefimenko's equations (named after Oleg D. Jefimenko) give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay (retarded time) of the fields due to the finite speed of light and relativistic effects.
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law [1] of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called the electrostatic force or Coulomb force. [2] Although the law was known earlier, it was first published in 1785 by ...
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).
In physics, specifically electromagnetism, the Biot–Savart law (/ ˈbiːoʊ səˈvɑːr / or / ˈbjoʊ səˈvɑːr /) [1] is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot–Savart law is ...