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 of the sheet is proportional to

Options

A. `cos theta`
B. `cot theta`
C. `sin theta`
D. `tan theta`

Answer

D

Explanation

Electric field due to a charged conducting sheet of surface charge density `sigma` is given by `E=sigma/(e_0e_r)` .Where, `e_0` is the permittivity in vacuum and `e_r` is the relative permittivity of medium.Here, electrostatic force on B,`QE=(Q sigma)/(e_0e_r)` . In equilibrium,
`T cos theta=mq and T sin theta=(Q sigma)/(e_0e_r)` Thus `tan theta=(Q sigma)/(e_0e_1 mg) implies tan theta prop sigma`