Question

Two charges q and $- 3q$ are placed fixed on x – axis separated by distance d. where should a third charge 2q be placed such that it will not experience any force?

• A. $\frac{d - \sqrt{3}d}{2}$
• B. $\frac{d + \sqrt{3}d}{2}$
• C. $\frac{d + 3d}{2}$
• D. $\frac{d - 3d}{2}$

Answer 1

Answer: (B)

$\frac{d + \sqrt{3}d}{2}$

Answer 2

:

Let a charge 2q be placed at P, at a distance l from A where charge q is placed, as shown in figure. The charge 2q will not experience any force, when force of repulsion on it due to q is balanced by force of attraction on it due to -3q at B where AB =d

or $\frac{(2q)(q)}{4\pi\varepsilon_{0}l^{2}} = \frac{(2q)( - 3q)}{4\pi\varepsilon_{0}(l + d)^{2}}$

$(l + d)^{2} = 3l^{2}$

or $2p - 2ld - d^{2} = 0$

$\therefore l = \frac{2d \pm \sqrt{4d^{2} + 8d^{2}}}{4} = \frac{d}{2} \pm \frac{\sqrt{3}d}{2}$

$l = \frac{d + \sqrt{3}d}{2}$