Encyclopedia
Definition
In physics, there are two kinds of
dipoles . An
electric dipole is a separation of positive and negative charge. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some, usually small, distance. By contrast, a magnetic dipole is a closed circulation of electric current. A simple example of this is a single loop of wire with some constant current flowing through it.
Dipoles can be characterized by their
dipole moment, a vector quantity. For the simple electric dipole given above, the electric dipole moment would point from the negative charge towards the positive charge, and have a magnitude equal to the strength of each charge times the separation between the charges. For the current loop, the
magnetic dipole moment would point through the loop , with a magnitude equal to the current in the loop times the area of the loop.
In addition to current loops, the
electron, among other fundamental particles, is said to have a magnetic dipole moment. This is because it generates a
magnetic field which is identical to that generated by a very small current loop. However, to the best of our knowledge, the electron's magnetic moment is not due to a current loop, but is instead an intrinsic property of the electron. It is also possible that the electron has an
electric dipole moment, although this has not yet been observed
A permanent magnet, such as a bar magnet, owes its magnetism to the intrinsic magnetic dipole moment of the electron. The two ends of a bar magnet are referred to as poles , and are labeled "north" and "south." The dipole moment of the bar magnet points from its magnetic
south to its magnetic
north pole — confusingly, the "north" and "south" convention for magnetic dipoles is the opposite of that used to describe the Earth's geographic and magnetic poles, so that the Earth's geomagnetic north pole is the
south pole of its dipole moment.
The only known mechanisms for the creation of magnetic dipoles are by current loops or quantum-mechanical spin since the existence of magnetic monopoles has never been experimentally demonstrated.
Torque on a dipole
Since the direction of an electric field is defined as the direction of the force on a positive charge, electric field lines point away from a positive charge and toward a negative charge.
When placed in an
electric or
magnetic field, equal but opposite forces arise on each side of the dipole creating a
torque t:
for an electric
dipole moment p , or
for a magnetic dipole moment
m .
The resulting torque will tend to align the dipole with the applied field, which in the case of an electric dipole, yields a potential energy of
.
The energy of a magnetic dipole is similarly
.
Physical dipoles, point dipoles, and approximate dipoles
A
physical dipole consists of two equal and opposite point charges: literally, two poles. Its field at large distances depends almost entirely on the dipole moment as defined above. A
point dipole is the limit obtained by letting the separation tend to 0 while keeping the dipole moment fixed. The field of a point dipole has a particularly simple form, and the order-1 term in the multipole expansion is precisely the point dipole field.
Although there are no known magnetic monopoles in nature, there are magnetic dipoles in the form of the quantum-mechanical spin associated with particles such as
electrons . A theoretical magnetic
point dipole has a magnetic field of the exact same form as the electric field of an electric point dipole. A very small current-carrying loop is approximately a magnetic point dipole; the magnetic dipole moment of such a loop is the product of the current flowing in the loop and the area of the loop.
Any configuration of charges or currents has a 'dipole moment', which describes the dipole whose field is the best approximation, at large distances, to that of the given configuration. This is simply one term in the multipole expansion; when the charge is 0—as it
always is for the magnetic case, since there are no magnetic monopoles—the dipole term is the dominant one at large distances: its field falls off in proportion to , as compared to for the next term and higher powers of for higher terms, or for the monopole term.
Molecular dipoles
Many
molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. For example:
- H-Cl
A molecule with a permanent dipole moment is called a polar molecule and is
polarized. 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
debye 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.
Typical gas phase values of some chemical compounds in Debye units :
These values can be obtained from measurement of the dielectric constant. When the symmetry of a molecule cancels out a net dipole moment, the value is set at 0. The highest dipole moments are in the range of 10 to 11. From the dipole moment information can be deduced about the
molecular geometry of the molecule. For example the data illustrate that carbon dioxide is a linear molecule but ozone is not.
Field from a magnetic dipole
Magnitude
The strength,
B, of a dipole magnetic field is given by:
where:
- B is the strength of the field, measured in teslas
- r is the distance from the center, measured in metres
- ? is the magnetic latitude where ? = magnetic colatitude, measured in radians or degrees from the dipole axis
- M is the dipole moment, measured in ampere square-metres, which equals joules per tesla.
- µ0 is the permeability of free space, measured in henrys per metre.
Vector form
The field itself is a vector quantity:
where
- B is the field
- r is the vector from the position of the dipole to the position where the field is being measured
- r is the absolute value of r: the distance from the dipole
is the unit vector parallel to
r- m is the dipole moment
- µ0 is the permeability of free space
This is
exactly the field of a point dipole,
exactly the dipole term in the multipole expansion of an arbitrary field, and
approximately the field of any dipole-like configuration at large distances.
Magnetic vector potential
The vector potential
A of a magnetic dipole is
with the same definitions as above.
Field from an electric dipole
The electrostatic potential of an electric dipole is
And the
electric field from a dipole can be found from the
gradient of this potential:
where
- E is the electric field
- r, r, are as above
- p is the dipole moment
- e0 is the permittivity of free space.
Notice that this is formally identical to the magnetic field of a point magnetic dipole; only a few names have changed.
Dipole radiation
In addition to dipoles in electrostatics, it is also common to consider an electric or magnetic dipole that is oscillating in time.
In particular, a harmonically oscillating electric dipole is described by a dipole moment of the form where ? is the
angular frequency. In vacuum, this produces fields:
Far away , the fields approach the limiting form of a radiating spherical wave:
which produces a total time-average radiated power
P given by:
This power is not distributed isotropically, but is rather concentrated around the directions lying perpendicular to the dipole moment.
Usually such equations are described by
spherical harmonics, but they look very different.
A circular polarized dipole is described as a superposition of two linear dipoles.
See also
References
External links
