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Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m −3), at any point in a volume.
Gauss's law makes it possible to find the distribution of electric charge: The charge in any given region of the conductor can be deduced by integrating the electric field to find the flux through a small box whose sides are perpendicular to the conductor's surface and by noting that the electric field is perpendicular to the surface, and zero ...
The charges must have a spherically symmetric distribution (e.g. be point charges, or a charged metal sphere). The charges must not overlap (e.g. they must be distinct point charges). The charges must be stationary with respect to a nonaccelerating frame of reference. The last of these is known as the electrostatic approximation. When movement ...
Charge quantization is the principle that the charge of any object is an integer multiple of the elementary charge. Thus, an object's charge can be exactly 0 e, or exactly 1 e, −1 e, 2 e, etc., but not 1 / 2 e, or −3.8 e, etc. (There may be exceptions to this statement, depending on how "object" is defined; see below.)
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
According to Gauss’s law, a conductor at equilibrium carrying an applied current has no charge on its interior.Instead, the entirety of the charge of the conductor resides on the surface, and can be expressed by the equation: = where E is the electric field caused by the charge on the conductor and is the permittivity of the free space.
The total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equation.