One end of a spring of negligible unstretched length and spring constant k is fixed at the origin $(0,0)$. A point particle of mass m carrying a positive charge q is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole $\vec{p}$ pointing towards the charge q is fixed at the origin, the spring gets stretched to a length $\ell$ and attains a new equilibrium position (see figure below). If the point mass is now displaced slightly by $\Delta \ell \ll \ell$ from its equilibrium position and released, it is found to oscillate at frequency $\frac{1}{\delta} \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$. The value of $\delta$ is $\_\_\_\_$ -