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The charge density appears in the continuity equation for electric current, and also in Maxwell's Equations. It is the principal source term of the electromagnetic field; when the charge distribution moves, this corresponds to a current density. The charge density of molecules impacts chemical and separation processes.
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 ...
We introduce the polarization density P, which has the following relation to E and D: = + and the following relation to the bound charge: = Now, consider the three equations: = = = The key insight is that the sum of the first two equations is the third equation.
According to Gauss’s law, a conductor at equilibrium carrying an applied current has no charge on its interior.Instead, the entirety of the charge of the conductor resides on the surface, and can be expressed by the equation: = where E is the electric field caused by the charge on the conductor and is the permittivity of the free space.
R is a region containing all the points at which the charge density is nonzero; r ' is a point inside R; and; ρ(r ') is the charge density at the point r '. The equations given above for the electric potential (and all the equations used here) are in the forms required by SI units.
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.
The equations introduce the electric field, E, a vector field, and the magnetic field, B, a pseudovector field, each generally having a time and location dependence. The sources are the total electric charge density (total charge per unit volume), ρ, and; the total electric current density (total current per unit area), J.
The Poisson–Boltzmann equation can also be used to calculate the electrostatic free energy for hypothetically charging a sphere using the following charging integral: = (′) ′ where is the final charge on the sphere The electrostatic free energy can also be expressed by taking the process of the charging system.