A) Only \[x=\sqrt{2}a\]
B) Only \[x=-\sqrt{2}a\]
C) Both \[x=\pm \sqrt{2}a\]
D) \[x=\frac{3a}{2}\] only
Correct Answer: B
Solution :
Suppose electric field is zero at a point P lies at a distance d from the charge + Q. At P \[\frac{kQ}{{{d}^{2}}}=\frac{k(2Q)}{{{(a+d)}^{2}}}\] Þ \[\frac{1}{{{d}^{2}}}=\frac{2}{{{(a+d)}^{2}}}\] Þ \[d=\frac{a}{(\sqrt{2}-1)}\] Since d > a i.e. point P must lies on negative x-axis as shown at a distance x from origin hence \[x=d-a\] \[=\frac{a}{(\sqrt{2}-1)}-a=\sqrt{2}\,a.\] Actually P lies on negative x-axis so \[x=-\sqrt{2}\,a\]You need to login to perform this action.
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