Question

Two point charges (+ Q) and (-2 Q) are fixed on the X-axis at positions a and 2a from origin respectively. At what positions on the axis, the resultant electric field is zero

• 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

Answer 1

The correct option is B Only $x=-\sqrt{2}a$

Suppose electric field is zero at a point P lies at a distance d from the charge + Q.
At P $\frac{kQ}{d^2}=\frac{k\left(2Q\right)}{(a+d{)}^2}$
$\Rightarrow \frac{1}{d^2}=\frac{2}{(a+d{)}^2}\Rightarrow d=\frac{a}{(\sqrt{2}-1)}$

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 $x=\sqrt{2}a$