Question

Two point charges $ -\text{ }q $ and $ +\text{ }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) $