Q. Two point charge $- q$ and $+ q/2$ are situated at the origin and at the point $(a,0,0)$ respectively. The point along the $X$-axis where the electric field vanishes is
A) $x = \frac{a}{\sqrt{2}}$
B) $x = \sqrt{2}a$
C) $x = \frac{\sqrt{2a}}{\sqrt{2} - 1}$
D) $x = \frac{\sqrt{2}a}{\sqrt{2} + 1}$
Explanation
(c) [image:1_image339.emf]
Suppose the field vanishes at distance $x,$ we have
$\frac{kq}{x^{2}} = \frac{kq/2}{(x - a)^{2}}$ or $2(x - a)^{2} = x^{2}$ or $\sqrt{2}(x - a) = x$
or $\left( \sqrt{2} - 1 \right)x = \sqrt{2}a$ or $x = \left( \frac{\sqrt{2}a}{\sqrt{2} - 1} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.