## Charge density definition

silly question i guess, but is charge density defined only for stationary charges?

i'm asking this because I did a couple homework problems on finding electric field in linear dielectric material. Dielectric is between two surfaces held at constant potential difference (ie. parallel plate, concentric sphere or cylinder.. well neglect fringe effects). From what I understand, there is no charge (free or induced) density in the dielectric material because they only occur on boundary between conductor and dielectric. So I solved the problems using Laplace's equation (instead of Poisson). I found there is constant current going through the dielectric material. Since current is flux of charges, there must be charges moving through dielectric. Those charges aren't in the charge density definition because they're acting as current or some other reason? Perhaps i'm confusing some issues here...

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 Blog Entries: 9 Recognitions: Homework Help Science Advisor $\rho_{el}\left(\vec{r},t\right)$ describes the volumic density of electric charge at the point $\vec{r}$ at the moment "t",no matter if the charge is moving or not... Daniel.
 my class is only on electrostatics.. so the $$\rho$$ in the equations below are static charges only? $$\nabla{^2} \cdot V = \frac{-\rho}{\epsilon}$$ $$\nabla \cdot E = \frac{\rho}{\epsilon}$$

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## Charge density definition

Yeah.Electrostatics means static fields created,obviously by time independent electric charge densities.

Daniel.

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 Quote by CrusaderSean my class is only on electrostatics.. so the $$\rho$$ in the equations below are static charges only? $$\nabla{^2} \cdot V = \frac{-\rho}{\epsilon}$$ $$\nabla \cdot E = \frac{\rho}{\epsilon}$$
Those equations apply to moving charges as well. Both of them are equivalent to one of Maxwell's Equations. In the presence of moving charge, however, that won't be enough to determine the electric field at a given point because it will have a non-zero curl.

 Blog Entries: 9 Recognitions: Homework Help Science Advisor Nope,for moving charges (in vacuum) we have $$\square V\left(\vec{r},t\right)=-\frac{\rho\left(\vec{r},t\right)}{\epsilon_{0}}$$ Daniel.

 Quote by SpaceTiger Those equations apply to moving charges as well. Both of them are equivalent to one of Maxwell's Equations...
i thought those equations were general (for static and dynamic) as well... guess i was wrong.

 Blog Entries: 9 Recognitions: Homework Help Science Advisor Gauss's law is the same (in mathematical form,not as functional dependence of the quantities involved) both for static & dynamic description. The potential's equation is diff,however...Poisson vs.d'Alembert... Daniel.

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