## Charge in Radial E-field (Potential Energy)

`$$ W_{\text{pot}} ~=~ \frac{ \class{red}{Q} }{4\pi \, \varepsilon_0} \, \frac{ \class{red}{q} }{r} $$`

$$F_{\text e} ~=~ \frac{1}{4\pi \varepsilon_0 \, \varepsilon_{\text r}} \, \frac{\class{red}{q_1} \, \class{blue}{q_2}}{r^2}$$ $$F_{\text e} ~=~ \frac{1}{4\pi \varepsilon_0 \, \varepsilon_{\text r}} \, \frac{\class{red}{q_1} \, \class{blue}{q_2}}{r^2}$$ $$\class{red}{q_1} ~=~ 4\pi \varepsilon_0 \, \varepsilon_{\text r} \, \frac{r^2 \, F_{\text e}}{\class{blue}{q_2}}$$ $$\class{blue}{q_2} ~=~ 4\pi \varepsilon_0 \, \varepsilon_{\text r} \, \frac{r^2 \, F_{\text e}}{\class{red}{q_1}}$$ $$r ~=~ \sqrt{ \frac{1}{4\pi \varepsilon_0 \, \varepsilon_{\text r}} \, \frac{\class{red}{q_1} \, \class{blue}{q_2}}{F_{\text e}} }$$ $$\varepsilon_{\text r} ~=~ \frac{1}{4\pi \varepsilon_0} \, \frac{\class{red}{q_1} \, \class{blue}{q_2}}{r^2 \, F_{\text e}}$$ $$\varepsilon_0 ~=~ \frac{1}{4\pi \varepsilon_{\text r}} \, \frac{\class{red}{q_1} \, \class{blue}{q_2}}{r^2 \, F_{\text e}}$$

Electrostatic force (also called Coulomb force) is the attractive or repulsive electric force between two charges \( q_1 \) and \( q_2 \).

This charge is the property of the first charge carrier participating in the electrical interaction. Depending on the sign of the charge, the charge carrier repels or attracts other charge carriers. A proton (positive sign) attracts an electron (negative sign).

This charge is the property of the second charge carrier that participates in the electrical interaction.

The distance between the charges \( q_1 \) and \( q_2 \). The larger this distance is, the smaller is the electrostatic force between the charges.

This dimensionless quantity describes the medium in which the two charges are located. If the two charges are in vacuum then \( \varepsilon_{\text r} = 1 \). And, if they are in water, for example, then \( \varepsilon_{\text r} = 80 \). The greater the relative permittivity of the medium, the more this medium weakens the force between the charges.

The vacuum permittivity is a physical constant that appears in equations involving electromagnetic fields. It has the following experimentally determined value:`$$ \varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}} $$`

**Copyright**: © 2022**License**: CC BY 4.0**Summary**: Formula with which you can calculate Coulomb force given two charges and their distance from each other.- This formula was added by Alexander Fufaev on
04/30/2022 - 10:59 . - This formula was updated by Alexander Fufaev on
11/26/2022 - 23:40 .