## Electric Charges and Fields

# Coulomb's Law and Forces between Multiple Charges

- Coulombs inverse square law \tt F = \frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q_{1}Q_{2}}{r^{2}}
- \tt \frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} N/m
^{2}& ε_{0}= 8.85 × 10^{−12}C^{2}/N-m^{2} - Coulombs law in vector form \tt \overline{F} = \frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q_{1}Q_{2}}{r^{2}} \times \hat{r}
- Dielectric constant or relative permittivity K is given by \tt K = \varepsilon_{r} = \frac{\varepsilon}{\varepsilon_{0}} = \frac{F air}{F medium}
- Coulombs electrostatic force is a conservative force
- Coulombs electrostatic force is a central force
- Principle of super position \tt \overline{F} = \overline{F}_{12} + \overline{F}_{13} + \overline{F}_{14} + ----

### View the Topic in this video From 27:31 To 40:23

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1. Electrostatic force of interaction acting between two stationary point charges is given by

F = \frac{1}{4 \pi \varepsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}

2. Forces between Multiple Charges

F_{1} = \frac{1}{4 \pi \varepsilon_{0}}\left[\frac{q_{1}q_{2}}{r_{12}^{2}} \hat{r}_{21} + \frac{q_{1}q_{2}}{r_{13}^{2}} \hat{r}_{31} + ...... + \frac{q_{1}q_{2}}{r_{n}^{2}} \hat{r}_{n 1}\right]