A spherical conducting shell of inner radius `r_1` and outer radius ` r_2 ` has a charge Q.
A charge q is placed at the centre of the shell. Find out the surface charge density on the inner and outer surface of the shell.
Is the electric field inside a cavity (with no charge ) zero. Independent of the fact wheather the shell is spherical or not ? Explain.

Explanation

When cahrge Q is given to spherical conducting shell, whole of it spreads uniformaly on the outer surface of shell. On placing a charge +q at the centre of the shell , a charge -q is induced on the inner surface of shell and in turn charge +q is induced on its outer surface.
` therefore ` Surface charge density of inner surface of the shell.
` " " sigma _("inner") =(-q)/( 4 pi r_1^(2)) `
and Surface charge density of outer surface of the shell.
` " " sigma _("outer") =((Q+q))/( 4 pi r_2^(2)) `
(ii) Electric field inside a cavity (with no charge) is always zero, whether the shell is spherical or of any other shape. It is accordance with Gauss.s theorem in electrostatics. As charge enclosed by the cavity is zero, hence total electric flux and consquently ,the field intensity inside a cavity must be zero.
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