Dipole

A dipole is a pair of electric charges or magnetic poles of equal magnitude but opposite polarity, separated by some (usually small) distance. Dipoles can be characterized by their dipole moment, a vector quantity with a magnitude equal to the product of the charge or magnetic strength of one of the poles and the distance separating the two poles. The direction of the dipole moment corresponds to the direction from the negative to the positive charge or from the south to the north pole. (Because of the absence of magnetic monopoles, magnetic dipoles are actually created by current loops or by quantum-mechanical spin.)

When placed in an electric (E) or magnetic (B) field, equal but opposite forces arise on each side of the dipole creating a torque τ:

τ = p × E (Electric dipole moment p)

τ = μ × B (Magnetic dipole moment μ)

(note: × corresponds to a vector cross product)

which will tend to align the dipole with the field.

Strictly speaking a dipole contains only two point charges (or magnetic poles), however various arrangements of multiple charges or currents have dipole moments and may be treated as an effective dipole. For the case of magnetic dipoles (where single magnetic monopoles do not exist naturally), the simplest dipole is a single ring of current, which will make a dipole field. Other more complicated systems can be approximated as dipole systems mathematically, especially if the net charge is zero, but the positive and negative charges are not distributed symmetrically and the dipole field structure is the dominant one.

The magnetic or electric field near a dipole decreases with distance (r) as 1/r² as opposed to the 1/r fall off of a monopole. The field which falls off proportionally to increasing powers of r are called the quadrapole component(1/r³) of the field, the octopole component (1/r⁴) of the field, and so on.

Many molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. For example:

 (positive) H-Cl (negative)

A molecule with a permanent dipole moment is called a polar molecule and is polarised. The physical chemist Peter J. W. Debye was the first scientist to study molecular dipoles extensively, and dipole moments are consequently measured in units named debyes in his honor.

With respect to molecules there are three types of dipoles:

• Permanent dipoles: These occur when 2 atoms in a molecule have substantially different electronegativity - one atom attracts electrons more than another becoming more negative, while the other atom becomes more positive. See dipole-dipole attractions.

• Instantaneous dipoles: These occur due to chance when electrons happen to be more concentrated in one place than another in a molecule, creating a temporary dipole. See Instantaneous dipole attraction.

• Induced dipoles These occur when one molecule with a permanent dipole repels another molecule's electrons, "inducing" a dipole moment in that molecule. See induced-dipole attraction.

Strength of a Dipole Magnetic Field

The strength of a dipole magnetic field where:

r = distance from the center

λ = magnetic latitude (90-θ) where θ = magnetic colatitude

M = dipole moment

is:

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From the point of view of the mathematics of distributions, a dipole can be taken to be the directional derivative of a Dirac delta function.