An infinite number of point charges, each carrying $1 μC$ charge, are placed along the y-axis at y = 1m, 2m, 4m, 8m_____. The total force on a 1C point charge, placed at the origin, is $x \times 10^{3} N$ . The value of x, to the nearest integer, is
$[Take \frac{1}{4 {πε}_{0}} = 9 \times 10^{9} {Nm}^{2} / C^{2}]$

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answer is 12.

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Detailed Solution

$\begin{array}{l} F_{total} = [\frac{{kq}_{1} q_{2}}{r_{1}^{2}} + \frac{{kq}_{1} q_{3}}{r_{2}^{2}} + \frac{{kq}_{1} q_{4}}{r_{3}^{2}} + \dots] \\ F = (k) (10^{- 6}) [\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{4^{2}} + \dots] \\ = \frac{(k) 10^{- 6}}{1 - \frac{1}{4}} = \frac{(9 \times 10^{9}) \times 4 \times 10^{- 6} N}{3} = 12 \times 10^{3} N \end{array}$