>[!summary] > The electric force is the force exerted by a charged particle > > **Key equations:** > Force by a charged particle: $F = \frac{q q_2}{4\pi R^2 \epsilon _0}$ >[!info]+ Read Time **⏱ 2 mins** # Definition The electric force is the force experienced by a charged particle due to another charged particle or by an [[Electric Fields|electric field]]. The electric force can be defined in two ways, by [[Coulomb's Law|Coulomb's law]], where you define the force by a charged particle. Or by the electric field, where you define the force due to an electric field. $ \begin{array}{c} \text{Coulomb's Law:} \\ \vec{F} = \frac{\vec{q_{1}} \vec{q_{2}}}{4\pi R^2 \epsilon _0} \\ \\ \text{By the electric field:} \\ \vec{F}=q \vec{E} \end{array} $ # Deriving The Electric Force >[!warning] Assumptions Assume that a point charge will be in an electric field so that [[Forces]] are true > Also, assume the following: > - The [[Electric Fields| electric field]] is defined as $F = q_1E$ > - From [[Coulomb's Law]] the electric force by a point charge is $E = \frac{q}{4\pi R^2 \epsilon _0}$ ![[el_2.png]] [^2] >[!note] Explanation A point charge in an electric field. $\begin{array}{c} \text{A point charge is in an electric field, the force on the point charge is equal to} \\ F = q_1E \\ \\ \text{From Coulombs Law we know:} \\ E = \frac{q_2}{4\pi R^2 \epsilon _0} \\ \\ \vec{F} = q(\frac{q_2}{4\pi R^2 \epsilon _0}) \\ \vec{F} = \frac{\vec{q_{1}} \vec{q_{2}}}{4\pi R^2 \epsilon _0} \end{array}$ --- > 💡 Found this concept helpful? [Star Math & Matter on GitHub](https://github.com/rajeevphysics/Obsidan-MathMatter) to support more intuitive science breakdowns like this. --- [^1]: Taken from https://tikz.net/charge/ by Izaak Neutelings (July 2018) [^2]: Taken from https://tikz.net/electric_field/ by Izaak Neutelings (July 2018)