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An infinite number of electric charges each equal to 5 nano-coulombs (magnitude) are placed along X-axis at $x = 1 cm, x = 2 cm, x = 4 cm, x = 8 cm$ ….and so on. In this setup if the consecutive charges have opposite sign, then the electric field at $x = 0$ $(\frac{1}{4 {πε}_{0}} = 9 \times 10^{9} N - m^{2} / c^{2})$

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$12 \times 10^{4} N / C$

$24 \times 10^{4} N / C$

$36 \times 10^{4} N / C$

$48 \times 10^{4} N / C$

answer is C.

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Detailed Solution

$E = E_{1} + E_{2} + E_{3} + ........$

$E = 9 \times 10^{9} [\frac{q}{r_{1}^{2}} + \frac{q}{r_{2}^{2}} + ....]$

$E = 9 \times 10^{9} \times \frac{5 \times 10^{- 9}}{10^{- 4}} [\frac{1}{1} - \frac{1}{4} + \frac{1}{16} - ....]$

$= 36 \times 10^{4} N / C$

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