Q. Infinite charges of magnitude $q$ each are lying at $x = 1,2,4,8\ldots meter$ on X-axis. The value of intensity of electric field at point $x = 0$ due to these charges will be
A) $12 \times 10^{9}q\ N/C$
B) Zero
C) $6 \times 10^{9}q\ N/C$
D) $4 \times 10^{9}q\ N/C$
Explanation
(a) Net field at origin $E = \frac{q}{4\pi\varepsilon_{0}}\left\lbrack \frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{4^{2}} + \ \ldots.\infty \right\rbrack$
$= \frac{q}{4\pi\varepsilon_{0}}\lbrack 1 + \frac{1}{4} + \frac{1}{16} + \ \ldots.\infty\rbrack$
$= \frac{q}{4\pi\varepsilon_{0}}\left\lbrack \frac{1}{1 - \frac{1}{4}} \right\rbrack = 12 \times 10^{9}q\ N/C$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.