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 o of the sheet is proportional to                  [AIEEE 2005]

A) \[\cos \theta \]

B) \[\cot \theta \]

C) \[\sin \theta \]

D) \[\tan \theta \]

Correct Answer: D

Solution :

[d] 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