Electrodynamics MOC

Charge continuity equation

The charge continuity equation is an expression of local conservation of charge relating the divergence of current to the depletion of charge.

Intuitively, if current is diverging from a point then that point must be losing charge. It is equivalent to the statement

(the flux of current through the surface of a solid is equal to the rate at which the solid loses charge) by applying Острогра́дский’s divergence theorem¹.

Derivation from Maxwell's equations

Taking the divergence of ^Differential and applying ^Differential

giving ^eq1.

This is an example of a continuity equation.

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Footnotes

1. 2023. Advanced Mathematical Methods, p. 39 ↩