Question

For what position of an electric dipole in a uniform electric field , its potential energy is minimum and maximum

Answer 1

The dipole has its least potential energy when it is in equilibrium orientation, which is when its momentum is lined up with Electric field (then τ = 0) It has greater potential energy in all other orientations. We are free to define the zero potential energy configuration in a perfectly arbitrary way , because only difference in potential energy have physical meaning. It turns out that the expression for the potential energy of an electric dipole in an external field is simplest if we choose the potential energy of the dipole to be zero when the angle it makes with electric field is 90°.

Thus U = 0 ; when ϕ is perpendicular to E U is minimum = -ϕ E ; when θ = 0° U is maximum = +ϕ E ; when θ = 180°

Answer 2

see in attachment mate.