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)  \[x=\sqrt{2a}\]

C)  \[x=\frac{\sqrt{2a}}{\sqrt{2-1}}\]                            

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

Correct Answer: C

Solution :

                Suppose the Field vanishes at a distance x, we have \[\frac{Kq}{{{x}^{2}}}=\frac{{{K}_{q/2}}}{{{(x-a)}^{2}}}\]                 or            \[2{{(x-a)}^{2}}={{x}^{2}}\]                 or            \[\sqrt{2}(x-a)=x\]                 or            \[(\sqrt{2}-1)x=\sqrt{2}a\]                 or            \[x=\frac{\sqrt{2}a}{\sqrt{2}-1}\]