Question

20 positively charged particles are kept fixed on the x-axis at points x=1m, 2m, 3m, ....., 20m. The first particle has a charge 1.0$\times {10}^{-6}C$, the second 8$\times {10}^{-6}C$, the third 27$\times {10}^{-6}C$ and so on. Find the magnitude of the electric force acting on a 1 C charge placed at the origin.

Answer 1

The magnitude of electric force acting on charge $Q_2$

$\because$ of charge $Q_1$ seperated by a distance $r$ is $F_{12}=\frac{1}{4\pi {ϵ}_{\circ }}\frac{Q_1{Q}_2}{r^2}$

Here the total force acting on $1\mu$C charge is

$F={\sum }_{n=1}^{20}\frac{{10}^{-12}}{4\pi {ϵ}_{\circ }}\frac{n^3}{n^2}$

$=\frac{{10}^{-12}}{4\pi {ϵ}_{\circ }}{\sum }_{n=1}^{20}n$

$={10}^{-12}\times 9\times {10}^9\times 210=1.89$N