Physics - Electrostatics Question with Solution | TestHub

In figure there is the schematic diagram of distribution of charges on $x$-axis Using principle of superposition total force acting on 1 C charge $$\begin{array}{rl}F& =\frac{1}{4\pi {\epsilon }_0}[\frac{1\times 1\times 10^{-6}}{(1{)}^2}+\frac{1\times 1\times 10^{-6}}{(2{)}^2}\\ & +\frac{1\times 1\times 10^{-6}}{(4{)}^2}+\frac{1\times 1\times 10^{-6}}{(8{)}^2}+\dots \infty ]\\ =& \frac{10^{-6}}{4\pi {\epsilon }_0}\left[\frac{1}{1}+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\dots \infty \right]\\ =& 9\times 10^{-6}\times 10^9\left(\frac{1}{1-\frac{1}{4}}\right)\\ =& 9\times 10^9\times 10^{-6}\times \frac{4}{3}=12000\mathrm{N}\end{array}$$