Question

Point charges are placed at the vertices of a square of side L as shown in figure. what should be sign of charge q and magnitude of the ratio |q/Q| so that

(a) net force on each Q is zero?

(b) net force on each q is zero?

(c) Is it possible that the entire system could be in electrostatic equilibrium?

Answer 1

(a)

$k\frac{qQ}{a^2}\cdot \frac{\sqrt2}{2}\cdot2-k\frac{QQ}{({a\sqrt{2}})^2}=0\to \frac{q}{Q}=\frac{1}{2\sqrt2}$

the sign of $q$ should be the negative of $Q.$

(b)

$k\frac{qQ}{a^2}\cdot \frac{\sqrt2}{2}\cdot2-k\frac{qq}{({a\sqrt{2}})^2}=0\to \frac{q}{Q}=2\sqrt2$

the sign of $q$ should be the negative of $Q.$

(c)

The entire system cannot be in equilibrium since both conditions i.e.

$q=-\frac{Q}{2\sqrt2}$

and

$Q=-\frac{q}{2\sqrt2}$

cannot be satisfied together.