the question is above.
Why do you think there is a problem with this?
Just going off what I recall. If we picture the atom as a single proton with a single electron in "orbit" around it, we can model the electron's orbit as a constant current, since it's moving so quickly around the atom. This essentially causes the magnetic moment of the atom.
However, the electric dipole moment is caused from an electric dipole (i.e. a separation between positive and negative charge). Now picture this same atom with the electron. The separation between the pos. and neg. charge is constantly changing direction (i.e. electric dipole is a vector.), and the average (if you wish) is just zero. Perhaps a second way is to imagine the electron as an electron "cloud" that surround the atom, then it's obvious that the dipole moment is zero.
If however, we apply an electric field, and separate this electron "cloud" a bit in a certain direction from the proton, we induce an electric dipole moment. (Read: dielectric).
This is essentially a classical model, and as such, can't be read into too greatly, other than to obtain a general picture of why.
As for jtbell's response... very thorough.
I had the impression that he thinks that there is something inconsistent about having a zero electric dipole moment but a nonzero dipole moment, and wanted him to clarify what was actually bothering him. I've been "burned" before by giving answers that turned out not to address what the questioner was really looking for.
There is another point about quantum electric vs magnetic dipole moments: EDM violates CP symmetry, while MDM does not. Recall that CP symmetry is just a symmetry of nature that says that you can flip the spins and the charges of the particle and you end up with the same physical system. QED is a theory that conserves CP, and therefore you can not generate an EDM by throwing photons around, while you can (and do!) generate a MDM.
Now the weak nuclear force does violate CP, and therefore you might imagine that these interactions can generate an EDM. However, if you perform the calculation, you can show that the generated quantum EDM is incredibly tiny, especially on atomic scales. I am not sure, but I do not think that there is a very good explanation for why the electron's EDM is so small (accidental cancellations, etc), although I am not an expert, and perhaps there are better explanations than I know of.
Many theories of new physics (such as supersymmetry, technicolor, etc) predict potentially large contributions to quantum EDMs, and this can provide a strong experimental constraints. Fun stuff! ;-)
Hope this helps!
"Why" questions are tough unless you are able to be quite specific in your context. In physics and science in general all "why" answers are contingent pushing the issue farther back. This is because the tool to answer questions in science is empirical observations. They tell us more "what happens" rather than why it happens at the fundamental level.
Looking at atoms one sees first that we have electrically charged particles with no magnetic charges. We note also that the positively and negatively charged particles have masses distinct by some orders of magnitude. This implies the orbital magnetic moment of the electron will not in general be canceled by the orbital magnetic moment of the nucleus (each about the center of mass of the atom.) On the other hand positronium consisting of an electron and positron in mutual orbit about a center will in principle have no magnetic moment in the ground state (above the state above mutual annihilation).
So that's sort of a "why" for the existence of the magnetic dipole moment in most atoms.
As for the electric dipole moment, in the absence of magnetic charges (which would create orbital electric dipole moments) an electric dipole moment can only be created by displacements of the average positions of the positive and negatively charged nucleus and electrons respectively. Since this leads to an internal net restoring force between them it can only occur either momentarily or as the result of an external electrical force polarizing the atom.
So indeed atoms may have a net electric dipole moment but only in the presence of an external electric field. Also you should check to see if in fact the example of Helium-4 doe or does not have a zero magnetic moment... (I don't recall at present.)
Actually, protons, neutrons and electrons have non-zero spin ("magnetic charge").
This is somewhat misleading, in that it doesn't make clear what happens when you look at a molecule (most matter is either crystalline, amorphous or molecular, and very, very rarely monoatomic). Most molecules do have a net electric dipole moment in the absence of an applied electric field.
"spin" is not really "magnetic charge". The phrase "magnetic charge" refers to magnetic monopoles, which (so far as we know) do not exist. Spin is the source for a "spontaneous magnetic dipole," it's true. But I wouldn't call it charge.
As you say, any time you have an asymmetric distribution of charge, you can expect a dipole to appear. But even if you have a perfectly symmetric charge distribution (point particle, atomic ground state, etc) we find that you can still have an electric or magnetic dipole moment quantum mechanically. However, the electric dipole moment is vanishingly small due to symmetries, while the magnetic dipole moment is typically quite large (large enough to measure in a Physics-101 lab!)
As has been pointed out I was referring to magnetic monopole charge analogous to the electrical monopole charges. This is the critical magnetic<=>electric asymmetry which the original posting seemed to invoke in its question.
In a molecule you do have applied electric field around the component atoms in so far as you can describe the atoms independently. This is distinct from an atom treated as an independent particle. Molecules bond when their electron "clouds" overlap substantially enough that there are in fact electrical fields within each atom induced by the radial fields between electron "cloud" and nucleus of the other.
 Let me add that in the context of the original post we were not talking about "most matter" but rather about individual atoms.
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