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An infinite number of point charges, each carrying 1 \mu C cagrge, are placed along the y-axis at y=1m, 2m, 4m .8m _____ The total force on a 1 C point charge, placed at the origin is x \times 10^3 N.  The value of x, to the nearest interger is ________
Option: 1 12
Option: 2 6
Option: 3 3
Option: 4 12

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\begin{array}{l} F = k (1 C )(1 \mu C )\left[1+\frac{1}{2^{2}}+\frac{1}{4^{2}}+\frac{1}{8^{2}}+\ldots\right] \\ \\ =9 \times 10^{3}\left[\frac{1}{1-\frac{1}{4}}\right]=12 \times 10^{3} N \end{array}

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Deependra Verma

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