Electricdipole

An electric dipole is a system consisting of two equal and opposite electric charges separated by a short distance. The dipole moment p is defined as p = q d, a vector pointing from the negative charge to the positive charge. For a general arrangement of charges, p = ∑ q_i r_i; in the simple two-charge model with charges +q and −q separated by d, p = q d.

In an external electric field E, the potential energy of a dipole is U = −p · E, and a torque τ = p × E tends to align the dipole with the field. In the far field, where the separation is small compared with the observation distance, the electric potential is V(r) ≈ (1/4πε0) (p · r̂)/r^2, and the electric field is E(r) ≈ (1/4πε0) [3 r̂ (p · r̂) − p] / r^3.

Dipole moments are central to describing molecular polarity and dielectric behavior. Polar molecules have permanent dipole moments, while nonpolar molecules may have zero net dipole moment due to symmetry. The water molecule is a classic example with a sizable dipole moment (~1.85 Debye, about 6.17×10^−30 C·m). Linear nonpolar molecules like CO2 have very small or negligible net dipole moments in equilibrium.

Applications include spectroscopy and molecular chemistry, where the dipole moment governs microwave and rotational transitions; in dielectric theory, the collective orientation of molecular dipoles under an external field explains polarization and dielectric constants. Measurements of dipole moments help characterize molecular structure and intermolecular interactions.