1. Interaction Force Between Plates

We have two plates with charges $Q_1 = +3q$ and $Q_2 = -2q$. The distance is small, so we treat them as infinite sheets for the field calculation.

The electric field produced by plate 2 affecting plate 1 is: $$ E_2 = \frac{\sigma_2}{2\epsilon_0} = \frac{|Q_2|}{2A\epsilon_0} = \frac{2q}{2A\epsilon_0} = \frac{q}{A\epsilon_0} $$ The force exerted on plate 1 is: $$ F_{\text{total}} = Q_1 E_2 = (3q) \left( \frac{q}{A\epsilon_0} \right) = \frac{3q^2}{A\epsilon_0} $$

Alternatively, using the mutual force formula $F = \frac{Q_1 Q_2}{2A\epsilon_0}$ is valid for the interaction, but we must be careful with unequal charges. The rigorous method is $F = Q_{target} \times E_{source}$. Both methods yield: $$ F_{\text{attraction}} = \frac{(3q)(2q)}{2A\epsilon_0} = \frac{3q^2}{A\epsilon_0} $$

2. Force per Rod

The total attractive force is balanced by the equal compressive force in the 3 insulating rods placed between the corners.Taking torque about a line passing through the centroid in the plane of triangle, the torque of electric forces would be zero, hence the forces in rods must be equal

$$ F_{\text{rod}} = \frac{F_{\text{total}}}{3} $$ $$ F_{\text{rod}} = \frac{1}{3} \left( \frac{3q^2}{A\epsilon_0} \right) $$