Question

Two point charges $-q$ and $+q/2$ are situated at the origin and the point $(a,0,0)$ respectively. The point along the x-axis, where the electric field vanishes is

• A. $x=\sqrt{2}a$
• B. $x=\frac{a}{\sqrt{2}}$
• C. $x=\frac{\sqrt{2}a}{\sqrt{2}-1}$
• D. $x=\frac{\sqrt{2a}}{\sqrt{2}+1}$

Answer 1

Answer: (C)

$x=\frac{\sqrt{2}a}{\sqrt{2}-1}$

The given situation can be shown as given
Suppose the field vanished at a distance $x$, we have
$\frac{kq}{x^2}=\frac{kq/2}{{(x-a)}^2}$
$\Rightarrow 2{(x-a)}^2=x^2$
$\sqrt{2}(x-a)=x$
$\Rightarrow \sqrt{2}x-x=\sqrt{2}a$
$\Rightarrow (\sqrt{2}-1)x=\sqrt{2}a$
$\Rightarrow x=\frac{\sqrt{2}a}{\sqrt{2}-1}$