dipoles

A dipole is a system consisting of two equal and opposite charges separated by a finite distance. The concept also extends to magnetic dipoles, which arise from a loop of current or from intrinsic spin and produce a magnetic moment.

For an electric dipole with charges +q and -q separated by distance d, the dipole moment is p = q d, a vector directed from the negative to the positive charge.

In an external electric field E, a dipole experiences a torque τ = p × E and has potential energy U = - p · E. Consequently, the dipole tends to align with the field, especially when rotation is allowed and the charges are not bound rigidly.

When distances are large compared to the separation, a charge distribution can be approximated by a point dipole. The far-field electric field of a point dipole falls off as 1/r^3 and depends on the orientation of p relative to the observation direction; the magnetic case has a corresponding 1/r^3 field with magnetic moment m.

In chemistry, the molecular dipole moment measures polarity and is usually expressed in Debye. It depends on bond polarity and molecular geometry. Water and ammonia are examples of polar molecules. Dipole moments influence solvation, boiling points, and molecular spectroscopy, and they help interpret infrared and microwave spectra.

Magnetic dipoles, generated by current loops or electron spins, interact with magnetic fields through torque and energy -m · B. The magnetic field of a dipole also decays as 1/r^3 and is used to model fields around small magnets and in precision measurements.