Two charges q (at A) and −3q(at B) are fixed on x-axis separated by distance d. Where should a third charge 2q be placed from A such that it will not experience any force?
Answer & explanation
Correct answer: option 1
Force on charge 2q should be equal to zero. Force on 2q should be equal and opposite due to q and -3q. For forces to be in opposite direction charge -2q cannot be placed between the two charges.
Let 2q is place at a distance x from A, then
$\frac{k.q.2q}{x^2} = \frac{k.2q.3q}{(d+x)^2}$
$ \frac{1}{x^2} = \frac{3}{(d+x)^2}$
$(d+x)^2 = 3x^2 \Rightarrow d+x = \sqrt{3}x$
$\Rightarrow d = (\sqrt{3}-1)x \Rightarrow x = \frac{d}{(\sqrt{3} -1)} = \frac{d(\sqrt{3}+1)}{2}$