Question

an infinite number of charges each equal to 4uC are placed along x-axis at x=1m,x=2m,x=4m and so on. find the electric potential at the origin due to the given set of charges.

Answer 1

Q =$4\mu C=4\times {10}^{-6}C,$x₁ = 1 m, x₂ = 2 m, x = 4 m
The value of electric potential at the origin V₁ = kq/r₁, V₂ = kq/r₂ , V₃ = kq/r₃,
According to superposition principle
$$\begin{gathered} \mathrm{V}={\mathrm{V}}_1+{\mathrm{V}}_2+{\mathrm{V}}_3 \\ \mathrm{V}=\frac{\mathrm{kq}}{{\mathrm{r}}_1}+\frac{\mathrm{kq}}{{\mathrm{r}}_2}+\frac{\mathrm{kq}}{{\mathrm{r}}_3} \\ \mathrm{V}=\mathrm{kq}\left[\frac{1}{{\mathrm{r}}_1}+\frac{1}{{\mathrm{r}}_2}+\frac{1}{{\mathrm{r}}_3}\right] \\ \mathrm{V}=9\times {10}^9\times 4\times {10}^{-6}\left[1+\frac{1}{2}+\frac{1}{4}\right] \\ \mathrm{V}=36\times {10}^{-3}\times 1.75=63\times {10}^{-3}\mathrm{V} \end{gathered}$$