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

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