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)

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