Question

An infinite number of point charges, each carrying $1\mu C$ charge, are placed along the y-axis at $y=1m,2m,4m,8m.\dots \dots$ The total force on a 1 C point charge, placed at the origin, is $x\times 10^{3}N$. The value of $x$, to the nearest integer, is_______.
[Take $\frac{1}{4\pi {ϵ}_0}=9\times 10^{9}N{m}^2/C^2]$

Answer 1

Answer: 12

$F=k(1C)(1\mu C)\left[1+\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{8^2}+\dots \right]$
$=9\times 10^3\left[\frac{1}{1-\frac{1}{4}}\right]=12\times 10^{3}N$