question_answer

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)  \[x=\frac{\sqrt{2a}}{\sqrt{2}+1}\]

Correct Answer: C

Solution :

 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 \[\sqrt{2}(x-a)=x\] \[\Rightarrow \] \[\sqrt{2}x-\sqrt{2}a=x\] \[\Rightarrow \] \[\sqrt{2}x-x=\sqrt{2}a\] \[\Rightarrow \] \[(\sqrt{2}-1)x=\sqrt{2}a\] \[\Rightarrow \] \[x=\left( \frac{\sqrt{2}a}{\sqrt{2}-1} \right)\]