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                                             [AIEEE 2005]

A)            \[\sin \theta \]

B)            \[\tan \theta \]

C)            \[\cos \theta \]

D)            \[\cot \theta \]

Correct Answer: B

Solution :

   \[T\sin \theta =qE\] and \[T\cos \theta =mg\] Þ \[\tan \theta =\frac{qE}{mg}=\frac{q}{mg}\,\left( \frac{\sigma }{2{{\varepsilon }_{0}}} \right)\] Þ \[\sigma \propto \tan \theta \].