A permanent dipole consists of a particle carrying a charge \(+q_{\mathrm{p}}\) at \(x=0, y=+\frac{1}{2} d\) and another particle carrying a charge \(-q_{\mathrm{p}}\) at \(x=0, y=-\frac{1}{2} d\). Use the electrostatic potential at a point \(\mathrm{P}\) on the axis of the dipole to determine the electric field at that point.