Four negatively charged particles each carry a charge \(q_{\mathrm{n}}\) and form a square of side length \(d\). A positively charged particle carrying a charge \(q_{\mathrm{p}}\) is at the square's center. If the arrangement is in equilibrium (the vector sum of the electric forces on each particle is zero), what is the numerical value of the ratio \(q_{\mathrm{p}} / q_{\mathrm{n}}\) ?