The bob of a pendulum of mass m, suspended by an inextensible string of length L as shown in the figure carries a small charge q. An infinite horizontal plane conductor with uniform surface charge density $$\sigma$$ is placed below it. What will be the time period of the pendulum for small amplitude oscillations?

A positive charge Q is situated at the centre of a cube. The electric flux through any face of the cube is (in SI units)

A charge of 0.8 coulomb is divided into two charges Q₁ and Q₂. These are kept at a separation of 30 cm. The force on Q₁ is maximum when

A particle with charge Q coulomb, tied at the end of an inextensible string of length R metre, revolves in a vertical plane. At the centre of the circular trajectory, there is a fixed charge of magnitude Q coulomb. The mass of the moving charge M is such that $$Mg = {{{Q^2}} \over {4\pi {\varepsilon _0}{R^2}}}$$. If at the highest position of the particle, the tension of the string just vanishes, the horizontal velocity at the lowest point has to be