Two metallic spheres of radii 1 cm and 3 cm are given charges of $$-$$1 $$ \times $$ 10^$$-$$2 C and 5 $$ \times $$ 10^$$-$$2 C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

Four point charges $$-$$Q, $$-$$q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is

What is the flux through a cube of side $$a$$ if a point charge of q is at one of its corner?

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle $$\theta $$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $$\theta $$ = 90^o, the torque and the potential energy of the dipole will respectively be