Electric charge is the conserved source of the electric field and the coupling carried by charged matter.
A system is charge neutral when its total positive and negative electric charge cancel.
Charge density is electric charge per unit volume, area, or length according to the dimension of its support.
A line charge is a charge distribution idealized as lying on a curve, described by charge per unit length. An infinite straight line with constant density produces the radial electric field by Gauss's law, and a logarithmic electrostatic potential.
The four-current combines charge density and current density into the four-vector . With , its four-divergence vanishes by the charge continuity equation: . It is the source in the covariant Maxwell equations.
A surface current density is electric current per unit transverse length confined to a surface. Integrating a thin layer's current density through its thickness gives .
A current sheet idealizes electric current as supported on a surface. It produces a jump in the tangential magnetic field.
For a surface current density on an interface with unit normal , Ampère's law givesin Gaussian units, or in SI units.
Surface conductivity is the conductivity of a thin layer integrated through its thickness. The sheet form of Ohm's law is .
A line current idealizes an electric current as flowing along a curve; its current-density volume integral reduces to along that curve.
Motional electromotive force is the contribution caused by a conductor moving through a magnetic field. The magnetic part of the Lorentz force separates charges within the conductor. For a bar of length moving at velocity perpendicular to a uniform field, its magnitude is ; the sign follows the chosen circuit orientation. Together with the electric-field contribution it enters Faraday's law for moving circuits.
For a smoothly moving circuit and a divergence-free magnetic field, the magnetic flux derivative is . The minus sign follows by orienting the swept side surface compatibly with the two spanning surfaces. Combining this transport identity with Faraday's law yields the moving-loop electromotive-force law.
Ohm's law states that the potential difference across an ohmic component equals its current times its resistance: .
Electrical electrical conductivity relates current density to the local electric field in the rest frame of an isotropic ohmic medium: . It is a bulk material coefficient, distinct from a sheet surface electrical conductivity. A moving conductor instead uses the moving-conductor Ohm law.
A material whose current density is proportional to its electric field, with proportionality given by its electrical conductivity.
In a homogeneous Ohmic conductor, the charge continuity equation and Gauss's law imply exponential decay of the bulk charge density, . For an isolated finite body, bulk charge moves to its boundary; the accumulating surface charge density preserves total electric charge. The formula uses a constant permittivity and the corresponding free-charge convention, or for total charge in the vacuum form of Gauss's law.
The Drude model describes classical charge carriers accelerated by an applied electric field and randomized by collisions of constant mean waiting time . Its mean drift obeys , and harmonic conductivity is in the negative-frequency exponential convention.
The Drude model relative permittivity is . At frequencies large compared with the collision rate but below , its leading real part is negative and the physical spatial wave-number branch has positive imaginary part. The field therefore decays into the conductor; close to the threshold the full complex response must be retained.
Joule heating converts electrical work into internal energy. A resistor dissipates ; in an ohmic continuum the local rate per volume is , with resistivity . Wind-driven currents are a proposed source of heating of an inflated giant planet.
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Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It is a scalar quantity and is responsible for electromagnetic phenomena. Electric charge exists in two types: positive and negative. 1. **Types of Charge**: - **Positive Charge**: Carried by protons, which are found in the nucleus of an atom. - **Negative Charge**: Carried by electrons, which orbit the nucleus of an atom.
