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)]

A pendulum has a bob of mass m carrying a positive charge q. Length of

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

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