This does not mean that individual positive and negative charges cannot be created or destroyed.
Electric charge is carried by subatomic particles such as electrons and protons.
Charge conservation was first proposed by British scientist William Watson in 1746 and American statesman and scientist Benjamin Franklin in 1747, although the first convincing proof was given by Michael Faraday in 1843.
[4][5] it is now discovered and demonstrated, both here and in Europe, that the Electrical Fire is a real Element, or Species of Matter, not created by the Friction, but collected only.Mathematically, we can state the law of charge conservation as a continuity equation:
is the electric charge accumulation rate in a specific volume at time t,
The integrated continuity equation between two time values reads:
The general solution is obtained by fixing the initial condition time
corresponds to the absence of charge quantity change in the control volume: the system has reached a steady state.
are equal (not necessarily constant) over time, then the overall charge inside the control volume does not change.
This deduction could be derived directly from the continuity equation, since at steady state
In electromagnetic field theory, vector calculus can be used 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).
The term on the left is the rate of change of the charge density ρ at a point.
The invariance of charge can be derived as a corollary of Maxwell's equations.
The left-hand side of the modified Ampere's law has zero divergence by the div–curl identity.
Expanding the divergence of the right-hand side, interchanging derivatives, and applying Gauss's law gives:
By the Gauss divergence theorem, this means the rate of change of charge in a fixed volume equals the net current flowing through the boundary: In particular, in an isolated system the total charge is conserved.
Charge conservation can also be understood as a consequence of symmetry through Noether's theorem, a central result in theoretical physics that asserts that each conservation law is associated with a symmetry of the underlying physics.
The symmetry that is associated with charge conservation is the global gauge invariance of the electromagnetic field.
[7] This is related to the fact that the electric and magnetic fields are not changed by different choices of the value representing the zero point of electrostatic potential
However the full symmetry is more complicated, and also involves the vector potential
The full statement of gauge invariance is that the physics of an electromagnetic field are unchanged when the scalar and vector potential are shifted by the gradient of an arbitrary scalar field
: In quantum mechanics the scalar field is equivalent to a phase shift in the wavefunction of the charged particle: so gauge invariance is equivalent to the well known fact that changes in the overall phase of a wavefunction are unobservable, and only changes in the magnitude of the wavefunction result in changes to the probability function
[8] Gauge invariance is a very important, well established property of the electromagnetic field and has many testable consequences.
The theoretical justification for charge conservation is greatly strengthened by being linked to this symmetry.
[citation needed] For example, gauge invariance also requires that the photon be massless, so the good experimental evidence that the photon has zero mass is also strong evidence that charge is conserved.
[9] Gauge invariance also implies quantization of hypothetical magnetic charges.
[10][11] Simple arguments rule out some types of charge nonconservation.
For example, the magnitude of the elementary charge on positive and negative particles must be extremely close to equal, differing by no more than a factor of 10−21 for the case of protons and electrons.
[12] Ordinary matter contains equal numbers of positive and negative particles, protons and electrons, in enormous quantities.
[13] The best experimental test comes from searches for the energetic photon from an electron decaying into a neutrino and a single photon: but there are theoretical arguments that such single-photon decays will never occur even if charge is not conserved.