question_answer

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

A) \[\cot \theta \]

B) \[\cos \theta \]

C) \[\tan \theta \]

D) \[\sin \theta \]

Correct Answer: C

Solution :

[c] \[T\sin \theta =\frac{\sigma }{{{\varepsilon }_{0}}K}.q\]                                  ?.(i) \[T\cos \theta =mg\]                                            ?(ii) Dividing (i) by (ii),  \[\tan \theta =\frac{\sigma q}{{{\varepsilon }_{0}}K.mg}\text{   }\therefore \sigma \propto \tan \theta \]