Q87 / 90 · JEE Main 2021 (18 Mar Shift 2) · Physics

An infinite number of point charges, each carrying $1 μ C$ charge, are placed along the y-axis at $y = 1 m, 2 m, 4 m, 8 m . . . .$
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 integer, is ___ .
[Take $\frac{1}{4 π ϵ_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}$ ]

Correct answer: 12

Solution

$F = k (1 C) (1 μ C) [1 + \frac{1}{2^{2}} + \frac{1}{4^{2}} + \frac{1}{8^{2}} + \dots]$

$= 9 \times 10^{3} [\frac{1}{1 - \frac{1}{4}}] = 12 \times 10^{3} N$

Hence, the correct answer is 12.