- #1

willDavidson

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- 6

- TL;DR Summary
- I am trying to understand what a point charge is.

I am trying to understand what a point charge is. Is it just an electron? Or is it just an idea?

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- Thread starter willDavidson
- Start date

- #1

willDavidson

- 50

- 6

- TL;DR Summary
- I am trying to understand what a point charge is.

I am trying to understand what a point charge is. Is it just an electron? Or is it just an idea?

- #2

A point charge ##q## at position ##\vec{r}_0## is described by a charge density consisting of a Dirac delta function, ##\rho(\vec{r}) = q\delta^{3}(\vec{r} - \vec{r}_0)##.

*Edit:* N.B. you can also check that this recovers the Coulomb law, i.e. from Maxwell I,$$\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}$$Perform a volume integral over a region ##\Omega## on both sides, and then use the divergence theorem on the LHS,$$\int_{\partial \Omega} \vec{E} \cdot d\vec{S} = \frac{1}{\varepsilon_0} \int_{\Omega} q\delta^3(\vec{r} - \vec{r}_0) dV = \frac{q}{\varepsilon_0}$$That's Gauss' law in integral form, which you can convert to Coulomb's law by choosing ##\partial \Omega## to be a spherical surface concentric with the point charge, of radius ##R##, $$4\pi R^2 E_r = \frac{q}{\varepsilon_0} \implies E_r = \frac{q}{4\pi \varepsilon_0 R^2}$$

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- #3

Kyouran

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