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)  cot \[\theta \]

C)  tan \[\theta \]                                 

D)  sin \[\theta \]

Correct Answer: C

Solution :

In equilibrium                 \[T\cos \theta =mg\]                                      ... (i) and        \[T=\sin \theta =F=Eq\]                 \[T\sin \theta =\frac{\sigma }{2{{\varepsilon }_{0}}}\cdot q\]                                      ... (ii) \[\therefore \]  \[\frac{T\sin \theta }{T\cos \theta }=\frac{\sigma q}{2{{\varepsilon }_{0}}\times mg}\]                 \[\tan \theta =\frac{\sigma q}{2{{\varepsilon }_{0}}mg}\] or            \[\sigma \propto \tan \theta \]