question_answer

A charged ball B hangs from a silk thread S, which makes an angle \[\theta \] with a large charged conducting sheet as shown in the figure. The surface charge density \[\sigma \] of the sheet is proportional to   AIEEE  Solved  Paper-2005

A) \[\cos \theta \]

B)                        \[\cot \theta \]

C)                        \[\sin \theta \]                 

D)        \[\tan \theta \]

Correct Answer: D

Solution :

Electric field due to a charged conducting sheet of surface charge density \[\sigma \] is given by \[E=\frac{\sigma }{{{\varepsilon }_{0}}\,{{\varepsilon }_{r}}}\,=\frac{l}{2{{\varepsilon }_{0}}}\] where,permittivity in vacuum andis relative permittivity of medium. Let the charge on the ball B is Q, then electrostatic force on it FBD of B is shown in figure. In equilibrium,                                                       ...(i) and                                              ...(ii) Thus, on dividing Eq. (ii) by Eq. (i), we get            or