Units of charge, Coulomb's Law
physics electricity electric charge Coulomb's law units # Landsberg - Elementary Textbook of Physics Vol 2 - Mir - 1988
Chapter 1 Electric Charges
1.11.1. What is the force of attraction between two unlike charges of \(\SI{1}{\micro\coulomb}\) \(\SI{1}{\micro\coulomb}\) each placed at a distance of \SI{0.3}{\meter} from each other?
The force of attraction \(F\) between two charges is given by
\begin{equation}
F = \frac{1}{4 \pi \epsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}
\end{equation}
in this case, \(q_{1} = q_{2} = 1 \, \mu C\) and \(r = \SI{0.3}{\meter}\). Hence
\begin{align}
F & = \frac{1}{4 \pi \epsilon_{0}}\frac{1 \, \mu \times 1 \, \mu \, C^{2}}{ (0.3 \, m)^{2}\, m^{2}}
& = \frac{9 \times 10^{9} \, N \, m^{2}/C^{2} \times 10^{-12} \, C^{2}} {9 \times 10^{-2} \, m^{2}}
& = 0.1 \, N
\end{align}
1.11.2. A pith ball suspended on a silk thread has a charge of $10 \, nC$. Another ball carrying the same charge is suspended at the same height at a certain distance from the first ball (Fig. 20). As a result of mutual repulsion, the balls diverge apart by $10\, cm$. By what angle are their threads declined from the vertical? The mass of each ball is $0.1\, g$.
Since the balls have the same charge they will repel each other with force given by Coulomb’s law. This force will create the divergence in the balls from the vertical, that is, the total force on the balls will be equal to sum of gravitational force acting vertically downwards and electric force acting horizontally. Let us first calculate the repelling force between the two balls given by Coulomb’s Law.
\(F = \frac{1}{4 \pi \epsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}\)
in this case, $q_{1} = q_{2} = 1 \, nC$ and $r = 10 \, cm$. Hence
\begin{align}
F & = \frac{1}{4 \pi \epsilon_{0}}\frac{10 \, \times 10 \, \, nC^{2}}{ (10 \, cm)^{2}\, m^{2}}
& = \frac{9 \times 10^{9} \, N \, m^{2}/C^{2} \times 100 \times 10^{-18} \, C^{2}} {100 \times 10^{-4} \, m^{2}}
& = 0.1 \, N
\end{align}