A uniform rod AB of mass m and length `l` is hinged at its mid point C. The left half (AC) of the rod has linear charge density `-lamda` and the right half (CB) has `+ lamda` where `lamda` is constant. A large non conducting sheet of uniform surface charge density `sigma` is also present near the rod. Initially the rod is kept perpendicular to the sheet. The end A of the rod is initialy at a distance d. Now the rod is rotated by a small angle in the plane of the paper and released. Prove that the rod will perform SHM and find its time period.

Answer

`T=2pi sqrt((2m in_(0))/(3 lambda sigma))`