Question

Infinite charges of magnitude $q$ each are lying at $x=1,2,4,8,........$ metre on X-axis. The value of intensity of electric field at point $x=0$ due to these charges will be

• A. $12\times {10}^{9}qN/C$
• B. $zero$
• C. $6\times {10}^{9}qN/C$
• D. $4\times {10}^{9}qN/C$

Answer 1

The correct option is A $12\times {10}^{9}qN/C$

$\begin{array}{c}Netfieldatorigin\\ E=\left[\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{4^2}+----\infty \right]\\ =\frac{q}{4\pi {\in }_0}\left[1+\frac{1}{4}+\frac{1}{16}+----\infty \right]\\ =\frac{q}{4\pi {\in }_0}\left[\frac{1}{1-\frac{1}{4}}\right]=12\times {10}^{9}qN/C\end{array}$

Hence,

option $\left(A\right)$ is correct answer.