The main thing to say is that magnetic dipole moment comes in two forms: one form owing to charges moving from one place to another (such as going around in a loop), and the other form intrinsic to certain kinds of entity and not related to motion. Many of the entities, such as electrons, which appear in the Standard Model of physics have the latter kind of dipole moment.

Your question suggests that the magnetic dipole moment of the electron might be of the first (motional) form. But the physical theory here says you would be wrong: the magnetic dipole moment of the electron is of the second (intrinsic) form. That is, it is simply part of the nature of what electrons are and it is not associated with any motion, whether displacement or rotation. On the other hand it is a sort of partner to the intrinsic angular momentum of the electron, and that property (also called spin) sounds as if motion is involved too, but in fact this is not so.

When we say that an electron has a dipole moment, what are we saying exactly? Basically it is a statement about how the electron interacts with other things, such as magnetic fields. Ultimately this property is deeply connected to the fundamental theory of what an electron is, and it is not possible to say much more about it in simple terms. You would have to learn about vector-like quantities called Dirac spinors and things like that. These spinors are simply the mathematical language of physical things such as electrons.

A note on classical physics for magnetic dipole moment angular momentum

Finally, let's add a note concerning the kind of scenario raised in your question. It does not concern electrons, but the more general question of the relationship between magnetic dipole moment $\bf \mu$ and angular momentum $\bf L$.

Can we have non-zero ${\bf L}$ for a zero $\bf \mu$? Yes: consider a neutral spinning object.

Can we have non-zero $\mu$ with zero $\bf L$? Yes: consider two rings or discs spinning about the same axis with equal and opposite angular momentum. There is then no angular momentum in total. Now make one of the rings charged and the other not. Then you have a magnetic dipole moment.

In conclusion, in classical physics, for a composite object, you can get any value of $g$. But for a point charged moving around a loop of any shape, the current around the loop and the area of the loop combine to make the angular momentum and magnetic dipole moment related to one another with $|g| = 1$.

The main thing to say is that magnetic dipole moment comes in two forms: one form owing to charges moving from one place to another (such as going around in a loop), and the other form intrinsic to certain kinds of entity and not related to motion. Many of the entities, such as electrons, which appear in the Standard Model of physics have the latter kind of dipole moment.

Your question suggests that the magnetic dipole moment of the electron might be of the first (motional) form. But the physical theory here says you would be wrong: the magnetic dipole moment of the electron is of the second (intrinsic) form. That is, it is simply part of the nature of what electrons are and it is not associated with any motion, whether displacement or rotation. On the other hand it is a sort of partner to the intrinsic angular momentum of the electron, and that property (also called spin) sounds as if motion is involved too, but in fact this is not so.

When we say that an electron has a dipole moment, what are we saying exactly? Basically it is a statement about how the electron interacts with other things, such as magnetic fields. Ultimately this property is deeply connected to the fundamental theory of what an electron is, and it is not possible to say much more about it in simple terms. You would have to learn about vector-like quantities called Dirac spinors and things like that. These spinors are simply the mathematical language of physical things such as electrons.

A note on classical physics for magnetic dipole and moment angular momentum

Finally, let's add a note concerning the kind of scenario raised in your question. It does not concern electrons, but the more general question of the relationship between magnetic dipole moment $\bf \mu$ and angular momentum $\bf L$.

Can we have non-zero ${\bf L}$ for a zero $\bf \mu$? Yes: consider a neutral spinning object.

Can we have non-zero $\mu$ with zero $\bf L$? Yes: consider two rings or discs spinning about the same axis with equal and opposite angular momentum. There is then no angular momentum in total. Now make one of the rings charged and the other not. Then you have a magnetic dipole moment.

In conclusion, in classical physics, for a composite object, you can get any value of $g$. But for a point charged moving around a loop of any shape, the current around the loop and the area of the loop combine to make the angular momentum and magnetic dipole moment related to one another with $|g| = 1$.

The main thing to say is that magnetic dipole moment comes in two forms: one form owing to charges moving from one place to another (such as going around in a loop), and the other form intrinsic to certain kinds of entity and not related to motion. Many of the entities, such as electrons, which appear in the Standard Model of physics have the latter kind of dipole moment.

Your question suggests that the magnetic dipole moment of the electron might be of the first (motional) form. But the physical theory here says you would be wrong: the magnetic dipole moment of the electron is of the second (intrinsic) form. That is, it is simply part of the nature of what electrons are and it is not associated with any motion, whether displacement or rotation. On the other hand it is a sort of partner to the intrinsic angular momentum of the electron, and that property (also called spin) sounds as if motion is involved too, but in fact this is not so.

When we say that an electron has a dipole moment, what are we saying exactly? Basically it is a statement about how the electron interacts with other things, such as magnetic fields. Ultimately this property is deeply connected to the fundamental theory of what an electron is, and it is not possible to say much more about it in simple terms. You would have to learn about vector-like quantities called Dirac spinors and things like that. These spinors are simply the mathematical language of physical things such as electrons.

The main thing to say is that magnetic dipole moment comes in two forms: one form owing to charges moving from one place to another (such as going around in a loop), and the other form intrinsic to certain kinds of entity and not related to motion. Many of the entities, such as electrons, which appear in the Standard Model of physics have the latter kind of dipole moment.

Your question suggests that the magnetic dipole moment of the electron might be of the first (motional) form. But the physical theory here says you would be wrong: the magnetic dipole moment of the electron is of the second (intrinsic) form. That is, it is simply part of the nature of what electrons are and it is not associated with any motion, whether displacement or rotation. On the other hand it is a sort of partner to the intrinsic angular momentum of the electron, and that property (also called spin) sounds as if motion is involved too, but in fact this is not so.

When we say that an electron has a dipole moment, what are we saying exactly? Basically it is a statement about how the electron interacts with other things, such as magnetic fields. Ultimately this property is deeply connected to the fundamental theory of what an electron is, and it is not possible to say much more about it in simple terms. You would have to learn about vector-like quantities called Dirac spinors and things like that. These spinors are simply the mathematical language of physical things such as electrons.

A note on classical physics for magnetic dipole moment angular momentum

Finally, let's add a note concerning the kind of scenario raised in your question. It does not concern electrons, but the more general question of the relationship between magnetic dipole moment $\bf \mu$ and angular momentum $\bf L$.

Can we have non-zero ${\bf L}$ for a zero $\bf \mu$? Yes: consider a neutral spinning object.

Can we have non-zero $\mu$ with zero $\bf L$? Yes: consider two rings or discs spinning about the same axis with equal and opposite angular momentum. There is then no angular momentum in total. Now make one of the rings charged and the other not. Then you have a magnetic dipole moment.

In conclusion, in classical physics, for a composite object, you can get any value of $g$. But for a point charged moving around a loop of any shape, the current around the loop and the area of the loop combine to make the angular momentum and magnetic dipole moment related to one another with $|g| = 1$.