Electromagnetic Dipoles
We use electromagnetic notations and nomenclature here (with SI units) because
that's the prime application,
but some of the discussion is really of a more general mathematical nature.
Dipole moments are what you get when something cancels in a small space with the
product change by space remaining constant.
An electric dipole is a charge into a length, a magnetic dipole is a
current into a surface area.
Peter
Debye |
(2008-05-16)
Electric Dipole Moment (EDM)
On the permanent EDM of asymmetrical molecules.
In 1912, Peter Debye (1884-1966)
pioneered the study of the electric dipole moments (EDM)
of asymmetrical molecules
(i.e., molecules without a center of symmetry).
He was awarded the Nobel prize for chemistry in 1936.
The unit of dipolar moment most commonly used by chemists
is the debye (D) which is defined as a decimal
submultiple of the franklin-centimeter,
the standard cgs unit (esu).
The franklin is a unit of electric charge
also known as statcoulomb (statC) and is worth exactly
0.1 C / 299792458.
One debye is equal
to one attofranklin-centimeter
(this particular use of a
metric prefix with a non-SI unit is especially dubious,
as the "atto" prefix was only introduced in 1975).
1 D = 10-18 statC.cm
=
(10-21 J/T) / c
=
3.33564095198... 10-30 C.m
As the elementary charge (e) is
1.602176487(40) 10-19 C,
an electric dipole moment (EDM)
of 1 D
corresponds to two opposite elementary charges separated by a distance of
about 0.2082 Å
(or 0.02082 nm).
Electric dipole moments of a few asymmetrical molecules :
| Molecule |
C.m |
Debye |
Charge | Displacement |
| Water, H2O |
6.17 10-30 |
1.85 D |
10 e | 3.9 10-12 m |
| Ammonia, NH3 |
4.90 10-30 |
1.47 D |
10 e | 3.1 10-12 m |
| Peroxide, H2O2 |
7.54 10-30 |
2.26 D |
18 e | 2.6 10-12 m |
| Hydrazine, N2H4 |
6.17 10-30 |
1.85 D |
18 e | 2.1 10-12 m |
| HCl |
3.60 10-30 |
1.08 D |
18 e | 1.2 10-12 m |
| CO |
0.374 10-30 |
0.112 D |
14 e | 0.17 10-12 m |
Hydrogen Peroxide
and Polarity by Vince Calder
Although many atoms have a permanent magnetic
moment, no permanent electric dipole moment (EDM)
has ever been detected for any atom.
In 2000, the search for a nonzero atomic EDM has led a team at the University of Washington
to one of the most precise measurements ever made
(cf.
Romalis et al., Phys. Rev. Lett. 86, 2505-2508).
The EDM of a mercury atom, if it has any,
would correspond to a displacement of its electronic cloud
(80 electrons) less than
2 10-30 m.
This is about 18 orders of magnitude less than what's
observed for the simple polar molecules
listed in the above table.
This result was obtained by looking for a possible shift due to strong electric fields of
the precession frequency of
199Hg atoms in a weak magnetic field.
No such frequency shift was observed at a precision of 0.4 nHz.
(2005-05-18)
Force exerted on a dipole by a nonuniform field
A uniform fields exerts a torque but no net force.
The net force an electric field E exerts on an electric dipole
p is:
F = grad (p.E)
- ( div E ) p
In the similar expression for the force exerted on a magnetic dipole m,
the second term vanishes because B
is divergence-free:
F = grad (m.B)
- ( div B ) m
= grad (m.B)
Originally, Coulomb defined what we now call the magnetic induction
B and the magnetic moment m
of a compass needle in terms of each other, using essentially the following
expression of the torque applied by the magnetic field to the needle.
He measured that mechanical torque directly
with the delicate torsion balance
which he invented. (Coulomb would later
use that instrument to establish the
basic law of electrostatics
which now bears his name.)
Torque on a Magnetic Dipole m
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Potential Energy of a Dipole m
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