If a small sphere of mass m and charge q hangs from a silk thread at angle `theta` with a charged coducting plate, show that the equilibrium of the sphere, the surface charge density for the plate is `epsilon_0 = (mg)/q tan theta`

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 Fig. Show that the surface charge density of the sheet is proportional to tan theta .

A 1 mg ball carrying a charge of 2xx10^-8 C hangs from a thread. When a large conducting plate of charge is brought near the ball, the thread makes an angle of 30^@ with the plate. What is the surface charge density of the plate?

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 muC//m^2 - Find the charge on the sphere.

A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of 100 muC/m^2 . Calculate the charge on the sphere.

A uniformly charged conducting sphere of 2.8 m in diameter has a surface charge density of 100muCm^-2 . Find the charge on the sphere.

Two small spheres each having mass m kg and charge q coulomb are suspended from a point by insultaing threads each l metre long but of negligible mass. If theta is the angle, each string makes with the vertical when equilibrium has been attained show that q^2 = (4m g l^2 sin ^2 theta tan theta) 4 pi upsilon_0

A small sphere of radius r_1 and charge q_1 is enclosed by a spherical shell of radius r_2 and charge q_2 . Show that if q_1 is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge q_2 on the shell is.

Two small spheres each of mass 10 mg are suspended from a poimt by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.28 m. If g = 10 ms^-2 , what is the charge on each ?

Show that the electric field at the surface of a charged conductor is given bu vecE = sigma/epsilon_0 hatn , where sigma is the surface charge density and hatn is a unit vector normal to the surface in the outward direction.