A charged sphere of radius r shares its charge with an uncharged sphere of radius `r_1`. Show that the ratio between the initial and the final energies of the two spheres is `(r+r_1)`:r.

Find the number of sphere of radius r touching the coordinate axes.

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 conducting spheres of radii r_1" and "r_2 are connected by a thin conducting wire.Some amount of charges is given to the system. The charge will be shared between them in such a way that the ratio between the surface densities of charge on the spheres is equal to

The volume of a solid sphere of radius 2r units is

Find the volume of the largest cylinder inscribed in the sphere of radius r cm.

find the volume of the largest cylinder inscribed in the sphere of radius r cm.

Two charged conducting spheres of radii r_1 and r_2 connected to each other by a wire. Find the ratio of electric fields at the surface of the two spheres.

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are