law of conservation of electric chargelaw
Conservation of electric charge is one of the fundamental pillars of physics, alongside conservation of energy. The idea that electricity is not created from nothing was first clearly expressed by Benjamin Franklin in the mid-18th century while studying static electricity. Later, Michael Faraday confirmed this in electrolysis experiments: the mass of substance deposited depends strictly on the passed charge. Modern physics explains the law through gauge symmetry (a certain kind of mathematical symmetry of the world), as proved by Emmy Noether.
How it works
The law works everywhere: from combing hair (transfer of electrons from one object to another) to nuclear reactions, where the total charge of particles before and after remains unchanged. In any closed system, where no charge enters from outside, the total electric charge is always constant.
💡 The most vivid example is the birth of an electron-positron pair from a photon. The particles appear from 'nothing', but the total charge remains zero: -1 for the electron and +1 for the positron.
\frac{\partial \rho}{\partial t} + \nabla \cdot \mathbf{J} = 0
ρ — electric charge density, J — current density, ∇· — divergence, ∂/∂t — partial derivative with respect to time. The equation expresses charge conservation: the change in charge within a volume equals the charge flux through the surface.