A pendulum has a bob of mass m carrying a positive charge q. Length of the pendulum string is L. Beneath the pendulum there is a large horizontal dielectric sheet of charge having uniform surface charge density of `sigma C//m^2`. [figure (i)] (a) Find the time period of small oscillations for the pendulum (b) Now the dielectric sheet of charge is tilted so as to make an angle `beta` with horizontal. Find the angle (a) that the thread makes with vertical in equilibrium position. Find time period of small oscillations in this case. [figure (ii)]

Answer

(a). `T=2pisqrt((L)/(g-(qsigma)/(2mepsilon_(0))))`
(b). `T=2pisqrt((L)/(sqrt(g^(2)+((qE)/(m))^(2)-2g(qE)/(m)cosbeta)))`