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## Main Question or Discussion Point

Currently, I am reading this article which introduces electromagnetism.

It gives a function for the charge density as: $$\rho = q\delta(x-r(t))$$

The paper states that "the delta-function ensures that all the charge sits at a point," but how does it do that? Also, if ##r(t)## is the trajectory of the electron, what is its purpose in the equation?

It gives a function for the charge density as: $$\rho = q\delta(x-r(t))$$

The paper states that "the delta-function ensures that all the charge sits at a point," but how does it do that? Also, if ##r(t)## is the trajectory of the electron, what is its purpose in the equation?