Coulomb's Law

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Table of Contents

• Coulomb’s Law
  • Key Definitions
  • Electrostatic Force
    • \(F_e=\frac{kq_1 q_2}{r^2}\space \left[N\right]\)
    • \(\vec{F}_{1,2}=k_e\frac{q_1 q_2}{r^2}\hat{r}_{2,1}\space \left[N\right]\)
    • \(k_e=\frac{1}{4\pi\epsilon_o}\approx9\times10^9\space\left[\frac{Nm^2}{C^2}\right]\)
      • \(\epsilon_o\approx8.854\times10^{-12}\space \left[\frac{C^2}{Nm^2}\right]\)
  • Multiple Charges
    • \(\vec{F}_{net}=\sum_{i=1}^{n}\vec{F}_i\)
    • \(\vec F_q=k_e q\sum_{i=1}^n\left(\frac{q_i}{r_i^2}\right)\hat r_i\)

#UCLA #Y1Q3 #Physics1B

Coulomb’s Law

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Key Definitions

Coulombs [$C$] - measure of

• $e^-\approx-1.602\times10^{-19}\space C$ Coulomb’s Law - the magnitude of electrostatic force between two point charges

Electrostatic Force

Coulomb’s Law - if two charges, $q_1$ and $q_2$, are separated by dist. $r$ :

\(F_e=\frac{kq_1 q_2}{r^2}\space \left[N\right]\)

E.g.

In vector form:

\(\vec{F}_{1,2}=k_e\frac{q_1 q_2}{r^2}\hat{r}_{2,1}\space \left[N\right]\)

E.g.

Coulomb’s Force Constant - the proportionality constant $k_e$

\(k_e=\frac{1}{4\pi\epsilon_o}\approx9\times10^9\space\left[\frac{Nm^2}{C^2}\right]\)

Where $\epsilon_0$ is the permittivity of free space

\(\epsilon_o\approx8.854\times10^{-12}\space \left[\frac{C^2}{Nm^2}\right]\)

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Multiple Charges

Principle of Superposition of Forces - allows the calculation of electrostatic force in any charge distribution

\(\vec{F}_{net}=\sum_{i=1}^{n}\vec{F}_i\)

E.g.

Generalized:

\(\vec F_q=k_e q\sum_{i=1}^n\left(\frac{q_i}{r_i^2}\right)\hat r_i\)