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_(0)mg)`
B. `(qsigma)/(4piepsilon_(0)mg)`
C. `(qsigma)/(4piepsilon_(0)mg)`
D. `(qsigma)/(epsilon_(0)mg)`

Answer

d

Explanation

Electric field due to charged conducting sheet, `E=(sigma)/(epsilon_(0))`
Let T be the tension in the string Ball is in equilibrium so
`Tcostheta=mg`
`Tsintheta=qE`
`therefore(Tsintheta)/(Tcostheta)=(qE)/(mg)`
`tantheta=(qE)/(mg)=(qsigma)/(epsilon_(0)mg)`