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An infinite number of charges each numerically equal to q and of the same sign are placed along the x-axis at $\;x=1 ,2 ,4 ,8----\;.$ Find elctric potential at $\;x=0$

$(a)\;k\;q\qquad(b)\;2 k\;q\qquad(c)\;4 k\;q\qquad(d)\;\large\frac{k\;q}{2}$

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Answer : (b) $\;2 k\;q$
Explanation :
$V= \large\frac{k\;q}{1}+ \large\frac{k\;q}{2} +\large\frac{k\;q}{4}+ \large\frac{k\;q}{8}+ \large\frac{k\;q}{16}+---$$
$V=k\;q\;[\large\frac{1}{1}+\large\frac{1}{2}+\large\frac{1}{2^2}+\large\frac{1}{2^3}+\large\frac{1}{2^4}+----]$
$V=\large\frac{k\;q\times1}{1-(\large\frac{1}{2})}=2\;k\;q\;.$
answered Feb 6, 2014 by yamini.v
edited Feb 6, 2014 by yamini.v
 

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