charge density: Definition from Answers.com

The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume. It is measured in coulombs per metre (C/m), square metre (C/m²), or cubic metre (C/m³), respectively. Since there are positive as well as negative charges, the charge density can take on negative values. Like any density it can depend on position. It should not be confused with the charge carrier density. As related to chemistry, it can refer to the charge distribution over the volume of a particle, molecule, or atom. Therefore, a lithium cation will carry a higher charge density than a sodium cation due to its smaller ionic radius.

1 Classical charge density
- 1.1 Homogeneous charge density
- 1.2 Discrete charges
2 Quantum charge density
3 Application
4 See also
5 References

Classical charge density

Homogeneous charge density

For the special case of a homogeneous charge density, that is one that is independent of position, equal to $ρ q,0$ the equation simplifies to:

$Q=V\cdot \rho_{q,0}$

The proof of this is simple. Start with the definition of the charge of any volume:

$Q=\int\limits_V \rho_q(\mathbf r) \,\mathrm{d}V$

Then, by definition of homogeneity, $\rho_q(\mathbf r)$ is a constant that we will denote $ρ q,0$ to differentiate between the constant and non-constant forms, and thus by the properties of an integral can be pulled outside of the integral resulting in:

$Q=\rho_{q,0} \int\limits_V \,\mathrm{d}V = \rho_{q,0} \cdot V$

so,

$Q=V \cdot \rho_{q,0}$

The equivalent proofs for linear charge density and surface charge density follow the same arguments as above.

Discrete charges

If the charge in a region consists of $N$ discrete point-like charge carriers like electrons the charge density can be expressed via the Dirac delta function, for example, the volume charge density is:

$\rho(\mathbf{r})=\sum_{i=1}^N\ q_i\delta(\mathbf{r} - \mathbf{r}_i)\,\!$ ;

where $\mathbf{r}\,\!$ is the test position， $q_i\,\!$ is the charge of the ith charge carrier, whose position is $\mathbf{r}_i\,\!$ .

If all charge carriers have the same charge $q$ (for electrons $q = - e$ ) the charge density can be expressed through the charge carrier density $n(\mathbf r)$ : Again, the equivalent equations for the linear and surface charge densities follow directly from the above relations.

Quantum charge density

In quantum mechanics, charge density is related to wavefunction $\psi(\mathbf r)$ by the equation

$\rho_q(\mathbf r) = q\cdot|\psi(\mathbf r)|^2$

when the wavefunction is normalized as

$Q= q\cdot \int |\psi(\mathbf r)|^2 \, d\mathbf r$

Application

The charge density appears in the continuity equation which follows from Maxwell's Equations in the electromagnetic theory.

References

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Donate to Wikimedia

	space-charge region (electronics)
	Lorentz-force density (electromagnetism)
	charge-density wave (solid-state physics)

	What is the physical meaning of charge density on lines or on areas? Read answer...
	When you adjust print density with laser printers you are adjusting the blank charge on the developing cylinder? Read answer...
	Given that gold is a univalent metal with a molar mass of 197 grams per mol and a density of 19.3 grams per cc how can the density of the charge carriers be calculated? Read answer...

	What is the physical significance of surface charge density 6.7?
	The density of charge is maximum at the pointed ends of a metallic conductor. Why?
	Describe the nucleus in terms of charge and density?

		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved. Read more
		Chemistry Dictionary. A Dictionary of Chemistry. Sixth Edition. Copyright © Market House Books Ltd, 2008. All rights reserved. Read more
		Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Charge density". Read more

charge density

Contents