Torque on Electric Dipole

The torque produced on an electric dipole by an electric field can be expressed as a vector product with direction given by the right hand rule.

The lever arm for each charge with respect to the center is

Energy of an Electric Dipole

An electric field produces a torque on a dipole which tends to take it to its low energy configuration. To rotate it from the low energy state against the field requires work

where the shorter form employs the scalar product.