JEE PYQ: Capacitance Question 7
Question 7 - 2021 (18 Mar Shift 2)
An infinite number of point charges, each carrying $1\mu$C charge, are placed along the y-axis at $y = 1$ m, 2 m, 4 m, 8 m …. 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 ____.
$\left[\text{Take } \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2\right]$
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Answer: 12
Solution
$F = k(1C)(1\mu C)\left[1 + \frac{1}{2^2} + \frac{1}{4^2} + \frac{1}{8^2} + \cdots\right] = 9 \times 10^3\left[\frac{1}{1-\frac{1}{4}}\right] = 12 \times 10^3$ N.
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