One end of a 10 cm long silk thread is fixed to a large vertical surface of a xharged nonconducting plate and the other end is fastened to a small ball having a mass of 10 g and charge of `4.0 xx 10^ C`. In equilibrium, the thread make an angle of `60^0` with the vertical. Find the surface charge dendity on the plate.

Explanation

T `cos 60^@` = mg
` T sin 60^@ = qE`
` tan 60^@ = qE/mg`
` E = (mg tan 60^@/q) = sigma/2epsilon_0`
` So, sigma = ((2 epsilon_0 mg tan 60^@)/q)`
` = (2 xx 8.8 xx (10^-12) xx 10 xx (10^-3) xx 9.8 xx 1.732/ 4.0 xx (10^-6))`
` =7.5 xx (10^-7) c/(m^2)` .