Question

An infinite number of charges, each equal to q, are placed along the x-axis at $x=1,x=2,x=4,x=8$ and so on. What is the potential at $x=0$ due to this set of charges?

Answer 1

Potential due to a single charge is given by
$V=\frac{1}{4\pi {\epsilon }_0}.\frac{q}{R}$
$\therefore$ Potential at $x=0$.
$V=v_1+v_2+v_3+\dots$
$=\frac{1}{4\pi {\epsilon }_0}.\frac{q}{1}+\frac{1}{4\pi {\epsilon }_0}.\frac{q}{2}+\frac{1}{4\pi {\epsilon }_0}.\frac{q}{4}+\frac{1}{4\pi {\epsilon }_0}q8$
$=\frac{q}{4\pi {\epsilon }_0}.\frac{1}{\left(\begin{array}{c}1-\frac{1}{2}\end{array}\right)}$
$=\frac{2q}{4\pi {\epsilon }_0}$