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An infinite number of electric charge each equal to 2 nano coulombs in magnitude are placed along X-axis at x = 1 cm, x = 3 cm, x = 9 cm, x = 27 cm…..and so on. In this setup, then the electric potential at x = 0 is

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1250 V

1350 V

2700 V

2500 V

answer is B.

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Detailed Solution

$V_{n e t} = \frac{1}{4 π ε_{0}} [\frac{q_{1}}{r_{1}} + \frac{q_{2}}{r_{2}} + ...]$

$= 9 \times 10^{9} [\frac{1}{1} - \frac{1}{3} + \frac{1}{9} - - -] \times \frac{2 \times 10^{- 9}}{10^{- 2}}$

$= 900 [\frac{1}{1 + \frac{1}{3}}] \times 2 (∴ \sum G P = \frac{a}{1 - r})$

$\frac{2700 \times 2}{40} = 1350 V$

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