question_answer

Two point charges \[-\,q\,\,and\,\,+q/2\] 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) \[x=\,\,\frac{\sqrt{2}a}{\sqrt{2}-1}\]                  

D) \[x=\,\,\frac{\sqrt{2}a}{\sqrt{2}+1}\]

Correct Answer: C

Solution :

Suppose the field vanishes at a (distance x), we have \[\frac{kq}{{{x}^{2}}}\,\,=\,\,\frac{kq/2}{{{(x-a)}^{2}}}\] \[or\,\,\,2{{(x-a)}^{2}}={{x}^{2}}\,\,\,\,\,or\,\,\,\,\sqrt{2}(x-a)=x\] \[or\,\,\,(\sqrt{2}-1)x=\sqrt{2}\,a\,\,\,\,\,or\,\,\,\,x=\left( \frac{\sqrt{2}\,a}{\sqrt{2}-1} \right)\]