Two particles with charges -q and +q , each having mass m , are attached to the ends of a light rod of length a to form a dipole. One end of the rod is clamped, and the system is positioned in a uniform electric field E such that the dipole axis is aligned with the field. The rod is given a slight tilt and subsequently released. Ignoring gravity, determine the time period of small oscillations.

Step-by-step solution

Let the clamped end of the rod be the origin of rotation. Since one end is clamped, the mass m at this end does not contribute to the moment of inertia. The moment of inertia of the system about the clamped end is due entirely to the mass at the free end, which is at a distance a : I = ma^2 When the dipole is in stable equilibrium, it is aligned with the uniform electric field E . If the rod is given a small angular displacement , the charge at the free end experiences an electric force F = qE . The restoring torqu