The amount of electric charge per unit volume or area in a material.Charge density is a measure of how much electric charge is concentrated in a given region of space, typically expressed per unit volume (volume charge density) or per unit area (surface charge density). It is a fundamental concept in electromagnetism, describing the distribution of positive and negative charges in materials, from conductors and semiconductors to plasmas and biological membranes. Understanding charge density is essential for predicting electric fields, potentials, and the behavior of charged particles in various media.
The concept of charge density emerged in the 18th century with the work of Benjamin Franklin and others on electric fluids, but it was formalized in the 19th century by James Clerk Maxwell, who incorporated it into his unified theory of electromagnetism.
Charge density is defined as the limit of charge per unit volume (or area) as the volume (or area) shrinks to a point. In a conductor, free charges redistribute to make the interior charge density zero, leaving all excess charge on the surface. In a dielectric, bound charges create a polarization charge density that modifies the net field. The concept enters directly into Maxwell's equations, particularly Gauss's law, which relates the electric field divergence to the charge density, and the continuity equation, which links charge density to current density.
Charge density is used in designing electronic devices, such as transistors and capacitors, in electrochemistry for battery design, and in medical imaging techniques like electrocardiography, where surface charge distributions on the heart are mapped.
In a typical lightning bolt, the charge density in the ionized channel can reach values on the order of 10^15 electrons per cubic meter, enough to heat the air to temperatures five times hotter than the Sun's surface.
| \rho_{\rm GJ} | variable | Goldreich-Julian charge density — charge density coulomb per cubic metre |
| \mathbf{\Omega} | variable | Angular velocity vector of the neutron star — angular velocity radian per second |
| \mathbf{B} | variable | Magnetic field vector — magnetic field tesla |
| c | constant | Universal constant, speed of light in vacuum — speed of light = 299792458 metre per second |
| 2\pi | constant | Mathematical constant, 2π — two pi = 6.283 |
| \cdot | operator | Scalar product of two vectors — dot product |
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