An infinite number of charges each equal to $0.2\,\mu C$ are arranged in a line at distances $1\,m, 2\,m, 4\,m, 8\,m......$ from a fixed point. The potential at fixed point is ......$kV$
Medium
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$\mathrm{V}=\sum \frac{\mathrm{kq}}{\mathrm{r}}$
$=9 \times 10^{9} \times 0.2 \times 10^{-6}\left[\frac{1}{1}+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots\right]$
$=1800\left[1+\frac{1}{2}+\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{2}\right)^{3}+\cdots\right]$
$=1800\left[\frac{1}{1-\frac{1}{2}}\right]=1800(2)=3600 \mathrm{\,V}$
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