Electric Dipole in a External Magnetic Field

Let's take an electric dipole, for example a molecule with a positive and negative charge. If we place it in a homogeneous electric field \(\class{purple}{\boldsymbol{E}}\) of a plate capacitor, then the negative charge experiences a force \(F_1\) towards the positively charged plate - that is against the electric field. The positive charge experiences a force \(F_2\) toward the negatively charged plate - along the electric field.

The dipole rotates until it is parallel to the electric field lines, such that the negative charge is on the side with the positive plate and the positive charge is on the side with the negative plate. In the final state, the torque on the dipole disappears and its energy becomes minimal. The resulting force on the dipole is then also zero in this state. In a homogeneous field, the electric dipole rotates but does not move!

Let us now generate an inhomogeneous electric field with a charged sphere. In this inhomogeneous field, the dipole will rotate until it is aligned along the field lines. If the charged sphere is positive, then the negative charge of the dipole turns toward the sphere because opposite charges attract. But if the sphere is negatively charged, then the positive charge of the dipole turns towards the sphere.

But something else happens in the inhomogeneous electric field besides rotation. The positive and negative charge of the dipole experience a different force along and against the field lines. To bring the two forces into equilibrium, the dipole shifts in the inhomogeneous E-field.