How does volume charge density relate to Gauss's law?

Gauss's law in differential form states ∇·E = ρ/ε₀, where ρ is volume charge density. This means the divergence of the electric field at any point equals the charge density there divided by the permittivity of free space. Positive ρ creates outward-pointing field; negative ρ creates inward-pointing field.

What are typical volume charge densities in nature?

Thunderclouds: ~1 nC/m³. Plasma in tokamaks: ~10⁻⁷ C/m³ (as electron density ~10²⁰ /m³ × e). Semiconductors vary with doping. In conductors at equilibrium, ρ = 0 inside (charge is on surface only). The ionosphere has ρ ~10⁻¹² C/m³.

Why is volume charge density zero inside a conductor?

In a conductor at equilibrium, free charges redistribute until the internal electric field is zero. By Gauss's law (∇·E = ρ/ε₀), if E = 0 everywhere inside, then ρ = 0 inside. All excess charge resides on the conductor surface. This is why Faraday cages work—charge stays on the outside, leaving the interior field-free.

How do I convert between electron density and charge density?

Multiply electron density (electrons/m³) by the elementary charge e = 1.602 × 10⁻¹⁹ C. For example, plasma with 10²⁰ electrons/m³ has charge density ρ = 10²⁰ × 1.602 × 10⁻¹⁹ = 16 C/m³ (if considering electrons only; net charge depends on ion density too).

Densité de charge volumique Converter

About Volume Charge Density Conversion

Volume charge density measures electric charge distributed throughout a three-dimensional region—coulombs per unit volume. It describes charge in bulk materials, plasmas, semiconductors, and any volumetric charge distribution in electrostatics and electrodynamics. Unlike surface or line charge densities which idealize charge on surfaces or lines, volume charge density represents real physical charge distributions in materials where charge is spread through a finite volume.

The SI unit is coulombs per cubic meter (C/m³). Volume charge density is fundamental to Maxwell's equations, appearing in Gauss's law in differential form: ∇·E = ρ/ε₀, where ρ is volume charge density. This equation states that electric field lines diverge from regions of positive charge and converge toward negative charge. In conductors at equilibrium, volume charge density is zero—all excess charge resides on the surface. Plasmas, doped semiconductors, and dielectrics under stress can maintain non-zero volume charge.

Our converter handles volume charge density units used in electromagnetism, plasma physics, and semiconductor device analysis.

Common Volume Charge Density Conversions

From	To	Multiply By
C/m³	μC/cm³	10⁻⁶
μC/cm³	C/m³	10⁶
C/m³	mC/m³	1,000
mC/m³	C/m³	0.001
C/m³	μC/m³	10⁶
C/m³	nC/cm³	10⁻³
C/m³	C/L	0.001
C/L	C/m³	1,000
nC/cm³	C/m³	0.001

Volume Charge Density Unit Reference

Coulomb per cubic meter (C/m³) – The SI unit for volume charge density. In most practical situations, values are quite small (μC/m³ to mC/m³) because even modest charge densities involve enormous numbers of elementary charges. One C/m³ corresponds to about 6.24 × 10¹⁸ elementary charges per cubic meter. Plasmas, charged aerosols, and semiconductors are analyzed using this unit.

Microcoulomb per cubic centimeter (μC/cm³) – Convenient for laboratory-scale experiments and demonstrations. 1 μC/cm³ = 1 C/m³ (note: the factors cancel). Used in electrochemistry, polymer electrets, and teaching examples where cm³ volumes are natural.

Coulomb per liter (C/L) – Practical for solution chemistry and electrochemistry. 1 C/L = 1000 C/m³. Ion concentration in electrolytes can be expressed this way, though molarity is more common.

Elementary charges per cubic meter (e/m³) – Standard in plasma physics where particle density matters more than charge per se. 1 e = 1.602 × 10⁻¹⁹ C. Typical electron densities: ionosphere 10¹⁰-10¹² /m³; glow discharge 10¹⁵-10¹⁸ /m³; tokamak fusion plasma 10¹⁹-10²⁰ /m³; solid matter ~10²⁹ /m³.

Nanocoulomb per cubic centimeter (nC/cm³) – Used for weakly charged materials and atmospheric electricity. Thundercloud charge density is roughly 1-10 nC/m³. Fair-weather atmospheric charge: ~10⁻¹² C/m³.