|
Charge conservation is the principle that electric charge can neither be created nor destroyed. The quantity of electric charge is always conserved. Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ...
In practice, charge conservation is a physical law that states that the net change in the amount of electric charge in a specific volume of space is exactly equal to the net amount of charge flowing into the volume minus the amount of charge flowing out of the volume. In essence, charge conservation is an accounting relationship between the amount of charge in a region and the flow of charge into and out of that same region.
Mathematically, we can state the law as
 where Q(t) is the quantity of electric charge in a specific volume at time t, QIN is the amount of charge flowing into the volume between time t1 and t2, and QOUT is the amount of charge flowing out of the volume during the same time period.
Formal statement of the law
More formally, we can use the concepts of vector and differential calculus to express the law in terms of charge density ρ (in coulombs per cubic meter) and electric current density J (in amperes per square meter): Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in two or more dimensions. ...
In mathematics, the derivative is one of the two central concepts of calculus. ...
Charge density is the amount of electric charge per unit volume. ...
The coulomb (symbol: C) is the SI unit of electric charge. ...
In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ...
In physics, the ampere (symbol: A, often informally abbreviated to amp) is the SI base unit used to measure electrical currents. ...
 . In the mid-nineteenth century, James Clerk Maxwell postulated the existence of electromagnetic waves as a result of his discovery that Ampere's law (in its original form) was inconsistent with the conservation of charge. After correctly reformulating Ampere's law, Maxwell also realized that such waves would travel at the speed of light, and that light itself must be a form of electromagnetic radiaton. See electromagnetic wave equation for a full discussion of these discoveries. James Clerk Maxwell (June 13, 1831–November 5, 1879) was a Scottish mathematical physicist, born in Edinburgh. ...
Electromagnetic radiation or EM radiation is a combination (cross product) of oscillating electric and magnetic fields perpendicular to each other, moving through space as a wave, effectively transporting energy and momentum. ...
In physics, Ampères law is the magnetic equivalent of Gausss law, discovered by André-Marie Ampère. ...
In physics, Ampères law is the magnetic equivalent of Gausss law, discovered by André-Marie Ampère. ...
Cherenkov effect in a swimming pool nuclear reactor. ...
The electromagnetic wave equation is a second-order partial differential equation that governs the propagation of electromagnetic waves through a medium. ...
Mathematical derivation The net current into a volume is  where S = ∂V is the boundary of V oriented by outward-pointing normals, and dS is shorthand for NdS, the outward pointing normal of the boundary ∂V. Here  is the current density (charge per unit area per unit time) at the surface of the volume. The vector points in the direction of the current flow. A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ...
From the Divergence theorem this can be written In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Ostrogradsky–Gauss theorem is a result that links the divergence of a vector field to the value of surface integrals of the flow defined by the field. ...
 . The net current into a volume must necessarily equal the net change in charge within the volume.  . Charge is related to charge density by the relation  . This yields  . Since this is true for every volume, we have in general - .
See also | 
Feeds |
Contact