Q 12-01-113JEE MainJEE Main 2021 (18 Mar, Shift 2)Easy
An infinite number of point charges, each carrying $1\ \mu\text{C}$ 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 $x\times10^3$ N. The value of $x$, to the nearest integer, is ______.
[Take $\dfrac{1}{4\pi\varepsilon_0} = 9\times10^9\ \text{N m}^2\text{ C}^{-2}$]
Numerical value type. Enter your answer.
Answer: 12
All forces act along the same line (repulsion along $-y$), so they add:
$$F = 9\times10^9\times10^{-6}\times1\left(1 + \frac14 + \frac1{16} + \dots\right) = 9\times10^3\times\frac{1}{1 - 1/4} = 12\times10^3\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics