Question 34 of 311

An infinite number of point charges, each carrying $1\mu C$ charge, are placed along the y-axis at $y=1m,2m,4m,8m....$
The total force on a $1C$ point charge, placed at the origin, is $x\times {10}^{3}N$. The value of $x$, to the nearest integer, is ___ .
[Take $\dfrac{1}{4\pi {ϵ}_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$]

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Answer: 12

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