The line AA' is on a charged infinite conducting plane which is perpendicular to the plane of the paper. The plane has surface density of charge `sigma` and B is a ball of mass m with a like charge of magnitude q. B is connected by a string from a point on the line AA'. The tangent of the angle `(theta)` formed between the line AA' and the string is (provided, the charge q does not affect the distribution of charge on conducting plate)

Options

A. `(qsigma)/(2epsilon_0mg)`
B. `(qsigma)/(4 pi epsilon_0mg)`
C. `(qsigma)/(2 pi epsilon_0mg)`
D. `(qsigma)/(epsilon_0mg)`

Answer

D

Explanation

`T sin theta =qE`
`T cos theta =mg`
`tantheta=(qE)/(mg)=(q.sigma/epsilon_0)/(mg) ` [As for conductor `E = sigma/(epsilon_0)` ]
`tantheta=(qsigma)/(epsilon_0mg)`