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