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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.
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.
Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m −3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.
Larmor formula; Lenz law; Liénard–Wiechert potential ... and ρ free is the free electric charge density. ... Proof that the formulations of Gauss's law in terms ...
ρ is the free electric charge density (in units of C/m 3) J is the current density J = ρ v {\displaystyle \mathbf {J} =\rho \mathbf {v} } with v as the velocity of the charges. The equation would apply equally to masses (or other conserved quantities), where the word mass is substituted for the words electric charge above.
which can be written in terms of free charge and bound charge densities (by considering the relationship between the charges, their volume charge densities and the given volume): = + Since within a homogeneous dielectric there can be no free charges ( ρ f = 0 ) {\displaystyle (\rho _{f}=0)} , by the last equation it follows that there is no ...
In this formulation, the divergence of this equation yields: = = +, and as the divergence term in E is the total charge, and ρ f is "free charge", we are left with the relation: =, with ρ b as the bound charge, by which is meant the difference between the total and the free charge densities.
J is the current density (with J tot being the total current including displacement current). [b] D is the displacement field (called the electric displacement by Maxwell). ρ is the free charge density (called the quantity of free electricity by Maxwell). A is the magnetic potential (called the angular impulse by Maxwell).