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Q.

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

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a

1350 V

b

1250V

c

2700V

d

2500 V

answer is B.

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Detailed Solution

$\begin{array}{l} V_{net} = \frac{1}{4 {πε}_{0}} [\frac{q_{1}}{r_{1}} + \frac{q_{2}}{r_{2}} + \dots .] \\ = 9 \times 10^{9} [\frac{1}{1} - \frac{1}{3} + \frac{1}{9} - - -] \times \frac{2 \times 10^{- 9}}{10^{- 2}} \\ = 900 [\frac{1}{1 + \frac{1}{3}}] \times 2 (∵ \sum GP = \frac{a}{1 - r}) \\ = \frac{2700 \times 2}{4} = 1350 V \end{array}$

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