Dipole in a Uniform External Field

Derive the equation for the couple acting on a electric dipole in a uniform electric field.

In a certain region of space, electric field is along the $z$-direction throughout. The magnitude of the electric field is, however, not constant but increases uniformly along the positive $z$-direction, at the rate of ${10}^5 \mathrm{N}/\mathrm{C}$ per meter. What are the force and torque experienced by a system having a total dipole moment equal to ${10}^{-7} \mathrm{Cm}$ in the negative $z$-direction?

An electric dipole with dipole moment $4 \times {10}^{-9} \mathrm{C} \mathrm{m}$ is aligned at ${30}^{°}$ with the direction of a uniform electric field of magnitude $5\times {10}^{4 }\mathrm{N} {\mathrm{C}}^{-1}$. Calculate the magnitude of the torque acting on the dipole.