First slide

Electric field

Question

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?

Moderate

A

$x = \sqrt{2} a$
B

$x = - \sqrt{2} a$
C

$x = \pm \sqrt{2} a$
D

$x = \frac{3 a}{2}$

Solution

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

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