An infinite number of electric charges, equal to 1C in magnitude, are placed along X-axis at x=2cm, 4cm, 8cm, so on. If they are of same sign, then electric potential at x=0 is (in volts)

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9 x 10¹¹

1.25 x 10⁹

3 x 10⁹

Zero

answer is A.

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Detailed Solution

$\begin{array}{l} V_{0} = V_{1} + V_{2} + \dots \\ = \frac{1}{4 {πε}_{0}} \cdot Q [\frac{1}{R_{1}} + \frac{1}{R_{2}} + \dots . +] \\ = \frac{9 \times 10^{9} \times (1)}{10^{- 2}} [\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots \dots .] \\ = \frac{9 \times 10^{9} \times (1)}{10^{- 2}} [\frac{1 / 2}{1 - (1 / 2)}] = 9 \times 10^{11} V \end{array}$

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