A point object of mass 1mg and charge `1muC` is hung with a silk thread at an angle `45^ ` with the surface of a vertical uniformly charged conducting plate. For equilibrium of object , the surface charge density (in SI unit) of the plate is (g= `10m//s^2`)

Options

A. `(10^4epsi_0)/(sqrt3)`
B. `10^4epsi_0`
C. `(10epsi_0)/(sqrt3)`
D. `10epsi_0`

Answer

D

Explanation

Use `F_E = qE " and " SigmaF=0` for equilibrium
From the F.B.D

`Tsin theta = qE`
`Tcos theta = qE`
`tan theta = (qE)/(mg)`
`(mg tan theta)/(q) = (sigma)/(epsi_0)`
`sigma = (epsi_0)/(q) mg tan theta`
`=(epsi_0)/(10^(-6)) xx10^(-6) xx10xx1=10epsi_0`