Magnetic Dipole - Internal Magnetic Field of A Dipole

Internal Magnetic Field of A Dipole

See also: Magnetic moment#Magnetic pole definition

The two models for a dipole (current loop and magnetic poles) give the same predictions for the magnetic field far from the source. However, inside the source region they give different predictions. The magnetic field between poles is in the opposite direction to the magnetic moment (which points from the negative charge to the positive charge), while inside a current loop it is in the same direction (see the figure to the right). Clearly, the limits of these fields must also be different as the sources shrink to zero size. This distinction only matters if the dipole limit is used to calculate fields inside a magnetic material.

If a magnetic dipole is formed by making a current loop smaller and smaller, but keeping the product of current and area constant, the limiting field is

.

where n=x/|x| is a unit vector, and δ(x) is the Dirac delta function in three dimensions. Unlike the expressions in the previous section, this limit is correct for the internal field of the dipole.

If a magnetic dipole is formed by taking a "north pole" and a "south pole", bringing them closer and closer together but keeping the product of magnetic pole-charge and distance constant, the limiting field is

These fields are related by B = μ0(H+M), where

is the magnetization.

Read more about this topic:  Magnetic Dipole

Famous quotes containing the words internal, magnetic and/or field:

    “A State, in idea, is the opposite of a Church. A State regards classes, and not individuals; and it estimates classes, not by internal merit, but external accidents, as property, birth, etc. But a church does the reverse of this, and disregards all external accidents, and looks at men as individual persons, allowing no gradations of ranks, but such as greater or less wisdom, learning, and holiness ought to confer. A Church is, therefore, in idea, the only pure democracy.”
    —Samuel Taylor Coleridge (1772–1834)

    “We are in great haste to construct a magnetic telegraph from Maine to Texas; but Maine and Texas, it may be, have nothing important to communicate.”
    —Henry David Thoreau (1817–1862)

    “The field of doom bears death as its harvest.”
    —Aeschylus (525–456 B.C.)