Question

An infinite number of charges 'q' each are placed along the x - axis at x =1, x=4 ,x=8 and so on. If the distance are in meters calculate the electric potential at x=0

• A. $\frac{3q}{8\pi E_0}$
• B. $\frac{q}{2\pi {ϵ}_0}$
• C. $\frac{2q}{\pi {ϵ}_0}$
• D. $\frac{4q}{\pi {ϵ}_0}$

Answer 1

The correct option is A $\frac{3q}{8\pi E_0}$

$\begin{array}{c}{V}_0=\frac{kq}{1}+\frac{kq}{4}+\frac{kq}{8}+.......................\\ =kq\left(1+\frac{1}{2^2}+\frac{1}{2^3}+..........\right)\\ =kq\left(1+\frac{\frac{1}{4}}{1-\frac{1}{2}}\right)\\ =kq\left(1+\frac{2}{4}\right)\\ =\frac{3kq}{2}=\frac{3q}{8\pi E_0}\end{array}$

Hence, Option $A$ is correct.