A uniformly charged half ring of a radius ' $R$ ' has linear charge density '$$\sigma$$'. The electric potential at the centre of the half ring is ( $$\epsilon_0=$$ permittivity of free space)

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. The surface charge density on the inner and outer surface of the shell will be

A charge of magnitude '2e' and mass '4m' is moving in an electric field $$\overrightarrow E $$. The acceleration imparted to the above charge is

Van de Graaff generator produces