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2. Electric Potential and Capacitance
medium
Electric charges having same magnitude of electricicharge $q$ coulombs are placed at $x=1 \,m , 2 \,m , 4 \,m$, $8 \,m$....... so on. If any two consecutive charges have opposite sign but the first charge is necessarily positive, what will be the potential at $x=0$ ?
A
Infinity
B
Zero
C
$\frac{1}{4 \pi \varepsilon_0}\left(\frac{2 q}{3}\right)$
D
$\frac{1}{4 \pi \varepsilon_0}(2 q)$
Solution
(c)
$\frac{k q}{1}-\frac{k q}{2}+\frac{k q}{4}-\frac{k q}{8}+\ldots \ldots$
$k q\left[1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\ldots \ldots\right]$
$\frac{k q \cdot 1}{1-\left(\frac{-1}{2}\right)}=V$
$V=\frac{2 k q}{3}$
Standard 12
Physics
