PX157 - A2 - coulomb's law

coulomb's law states that the force a charge, $q_{1}$ , at a location, ${\vec{r}}_{1}$ , exerts a force on charge, $q_{2}$ , at a location, ${\vec{r}}_{2}$ , that is given by:

{\vec{F}}_{12} = \frac{q_{1} q_{2}}{4 π ϵ_{0}} \frac{{\vec{r}}_{2} - {\vec{r}}_{1}}{| {\vec{r}}_{2} - {\vec{r}}_{1} |^{3}}

derivation

{\hat{r}}_{12} = \frac{{\vec{r}}_{2} - {\vec{r}}_{1}}{| {\vec{r}}_{2} - {\vec{r}}_{1} |}

{\vec{F}}_{12} = \frac{q_{1} q_{2}}{4 π ϵ_{0}} \frac{{\hat{r}}_{12}}{| {\vec{r}}_{2} - {\vec{r}}_{1} |^{2}}

where, $ϵ_{0} = 8.8542 \times 10^{- 12} F m^{- 1}$ (permittivity of free space)
$F$ (farad) $= C^{2} N^{- 1} m^{- 1}$

{\vec{F}}_{12} = \frac{q_{1} q_{2}}{4 π ϵ_{0}} \frac{{\vec{r}}_{2} - {\vec{r}}_{1}}{| {\vec{r}}_{2} - {\vec{r}}_{1} |^{3}}

{\vec{F}}_{g r a v, 12} = - m_{1} m_{2} G \frac{{\vec{r}}_{2} - {\vec{r}}_{1}}{| {\vec{r}}_{2} - {\vec{r}}_{1} |^{3}}

eg: hydrogen atom: proton and electron $\frac{| {\vec{F}}_{12} |}{| {\vec{F}}_{g r a v, 12} |} = \frac{e^{2}}{m_{p} m_{e}} \frac{1}{4 π ϵ_{0} G} = 2.39 \times 10^{39} >> 1$
electric force is much stronger than gravitational force, but the universe is dominated by the latter and not the former because most objects are electrically neutral