question_answer

A simple pendulum of lenght \[l\], has a bob of mass m with a charge q on it. A verticle sheet of charge with surface charge density Q, posses through the point of suspension. At equilibrium, the string makes an angle Q with the verticle then:

A)  \[\tan \theta =\frac{Qq}{2{{\varepsilon }_{0}}mg}\]

B)  \[\tan \theta =\frac{Qq}{{{\varepsilon }_{0}}mg}\]

C)  \[\cot \theta =\frac{Qq}{2{{\varepsilon }_{0}}mg}\]

D)  \[\cot \theta =\frac{Qq}{{{\varepsilon }_{0}}mg}\]

Correct Answer: A

Solution :

                    From the diagram             \[\tan \theta =\frac{Fe}{mg}=\frac{qE}{mg}\] As electric at near point due to a infinitely long thin sheet of charge is \[\frac{\sigma }{2{{\varepsilon }_{0}}}\] \[\Rightarrow \]               \[\tan \theta =\frac{qQ/2{{\varepsilon }_{0}}}{mg}=\frac{Qq}{2{{\varepsilon }_{0}}mg}\]