Charge conservation

Charge conservation refers to the physical fact of experience that in any closed system, the sum of the existing electric charge remains constant. When charged particles are created or destroyed, it is always in equal quantities of opposite sign.

In the sense of Noether 's theorem any conservation law is associated with a symmetry property of the respective theory, ie its invariance under gauge transformations. In the case of ( quantum ) electrodynamics which is the invariance under local gauge transformations ( gauge group U (1), multiplied by a complex phase factor) of the wave function of charged particles:

Corresponding charge conservation laws are also available for other gauge theories such as quantum chromodynamics ( conservation of color charge, associated gauge group SU (3 )) and the gauge theory of electro- weak interaction ( gauge group SU (2) x U (1 )), which in the Standard Model of elementary particle physics quantum electrodynamics generalized.

Derivation of the equation for the conservation of electric charge

As with the mass conservation ( continuity equation) can also be formulated as the charge conservation equation. It is derived in the following.

The current which flows from a volume V,

Being integrated over the edge S of the volume and the product is to be understood as an inner product of the current density vector with the normal vector of the surface.

With the integral theorem of Gauss follows:

And as the current flow out of the volume is equal to the rate of change of charge in the volume, is considered:

Charge and charge density are

Connected, so that we obtain:

Since the contiguous for each volume is considered, we finally obtain:

It is of the same mathematical form as the following from the mass conservation equation of continuity ( you only charge density by mass density, etc. to replace ).

The conservation of electric charge lies implicitly in the Maxwell equations:

Because the divergence of a rotation vanishes, follows on formation of the divergence of the second equation

If in this respect, the first time derivative of the equation, as follows

Usage

In apparent contradiction to the conservation of charge, the manner of speech of a charge generation is, for example, by friction. But that is a local accumulation of charges of one sign meant, ie a charge separation and not a " generation ".

• Physical basic concept
• Electrodynamics