question_answer

A charged ball hangs from a silk thread of length l.  It 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)  \[\cos \theta \]                         

B)  \[\cot \theta \]

C)  \[\sin \theta \]                         

D)  \[\tan \theta \]

Correct Answer: D

Solution :

From the diagram,             \[T\sin \theta =\frac{q\sigma }{2{{\varepsilon }_{0}}}\] and  \[T\cos \theta =mg\] \[\Rightarrow \]               \[\tan \theta \times \sigma \]