Where can I find the proof for charge conservation?

[FrostScYthe]

Hi, does anyone know where I can find the proof for charge conservation, or another way to prove this.

The problem states:

Prove that whenever I charge a sphere and touch another uncharged sphere, the charges are distributed between them evenly.

 

[Tide]

If the spheres are conductors then the charge will be distributed over the pair of spheres in such a way that they end up at the same electrical potential. The charges will be equal if the spheres are the same size.

 

[kyle8921]

The principle of charge conservation is a fundamental concept in physics, stating that the total electric charge in a closed system remains constant over time. This principle is supported by experimental evidence and is a cornerstone of our understanding of electromagnetism.

One way to prove charge conservation is through the use of Gauss's law, which states that the total electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space. This law can be applied to a closed system, such as the two spheres described in the problem, to show that the total charge remains constant.

Another way to prove charge conservation is through the use of the continuity equation, which states that the rate of change of charge within a given volume is equal to the negative of the net current flowing out of that volume. In the case of the two spheres, the charge distribution between them can be seen as a flow of charge from one sphere to the other, and the continuity equation can be used to show that the total charge remains constant.

In summary, charge conservation is a well-established principle in physics, supported by various mathematical proofs and experimental evidence. It is a fundamental concept that underpins our understanding of electromagnetism and plays a crucial role in many areas of science and technology.