Dipoles

	There's an interactive simulation available on the "Learning by Simulations" Web site which allows to visualize the electric field lines of one to four charges arbitrarily positioned on a plane.

A dipole field. Electric fields diverge from a positive charge and converge on a negative charge.

The simplest set of sources that can occur with electricity but not with gravity is the dipole, consisting of a positive charge and a negative charge with equal magnitudes. More generally, an electric dipole can be any object with an imbalance of positive charge on one side and negative on the other.

A water molecule, is a dipole because the electrons tend to shift away from the hydrogen atoms and onto the oxygen atom.

A water molecule is a dipole.

Your microwave oven acts on water molecules with electric fields. Let us imagine what happens if we start with a uniform electric field, (c), made by some external charges, and then insert a dipole, (d), consisting of two charges connected by a rigid rod. The dipole disturbs the field pattern, but more important for our present purposes is that it experiences a torque. In this example, the positive charge feels an upward force, but the negative charge is pulled down. The result is that the dipole wants to align itself with the field, (e). The microwave oven heats food with electrical (and magnetic) waves. The alternation of the torque causes the molecules to wiggle and increase the amount of random motion. The slightly vague definition of a dipole given above can be improved by saying that a dipole is any object that experiences a torque in an electric field.

What determines the torque on a dipole placed in an externally created field? Torque depends on the force, the distance from the axis at which the force is applied, and the angle between the force and the line from the axis to the point of application. Let a dipole consisting of charges +q and -q separated by a distance $ be placed in an external field of magnitude |E|, at an angle θ with respect to the field. The total torque on the dipole is

(Note that even though the two forces are in opposite directions, the torques do not cancel, because they are both trying to twist the dipole in the same direction.) The quantity $q is called the dipole moment, notated D. (More complex dipoles can also be assigned a dipole moment - they are defined as having the same dipole moment as the two-charge dipole that would experience the same torque.)

Dipole moment of a molecule of NaCl gas

The behavior of a dipole in an externally created field leads us to an alternative definition of the electric field:

Alternative definition of the electric field

The electric field vector, E, at any location in space is defined by observing the torque exerted on a test dipole D t placed there. The direction of the field is the direction in which the field tends to align a dipole (from - to +), and the field's magnitude is |E| = τ/D t sin θ.

The main reason for introducing a second definition for the same concept is that the magnetic field is most easily defined using a similar approach.