Two point charges $Q$ each are placed at a distance $d$ apart. A third point charge $q$ is placed at

Question

Two point charges $Q$ each are placed at a distance $d$ apart. A third point charge $q$ is placed at a distance $x$ from mid-point on the perpendicular bisector. The value of $x$ at which charge $q$ will be experience the maximum coulomb's force is

Professor PC Thomas Classes · Answer

Force $F = \frac{2kQq x}{(x^2 + (d/2)^2)^{3/2}}$. Maximizing $F$ by setting $dF/dx=0$ gives $x = \frac{d}{2\sqrt{2}}$.