The discussion centers around the concept of magnetic moments, particularly in the context of atoms and ions. Participants explore the definition, significance, and implications of magnetic moments, as well as their relationship to multipole expansions and dipole moments. The conversation includes theoretical aspects and touches on practical implications, with references to related phenomena such as the Zeeman effect.
Participants express varying levels of understanding and agreement on the definitions and implications of magnetic moments and dipole moments. There is no consensus on the clarity of these concepts, and multiple competing views remain regarding their relationships and significance.
Some participants indicate limitations in their mathematical background, which may affect their understanding of the multipole expansions discussed. The conversation also highlights the dependence on definitions and the complexity of visualizing certain concepts.
What do you mean by "the multipole expansion of a current distribution"? Magnetic moments are the same as dipole moments? (excuse my ignorance, but I'm not exactly sure what dipole moments are... In covalent bonds due to electronegativity and electropositivity, the bonded atoms develop a charge. Dipole moments apply to these situations, right? But where and what exactly is the dipole moment?)blue_leaf77 said:Magnetic (dipole) moment is just the first term in the multipole expansion of a current distribution. In an atom, electron moves with some velocity around the nucleus, therefore there must be a net current associated with this movement. The magnetic moment of a free atom does nothing upon itself, however its influence to the electronic states begins to emerge when the atom interacts with external magnetic fields. See also "Zeeman effect".
As you see there are electric dipole moment and magnetic dipole moment, but sometimes the first word is dropped and is assumed to be known form the context being discussed.Priyadarshini said:Magnetic moments are the same as dipole moments?
The dipole moment mentioned in this context must be the electric dipole moment. But of course one can also calculate the magnetic dipole moment of an atom or molecule.Priyadarshini said:In covalent bonds due to electronegativity and electropositivity, the bonded atoms develop a charge. Dipole moments apply to these situations, right?
The maths on the pdf link you provided was a wee bit confusing (I haven't learned integration or limits yet :/ ) But I get the general idea about the differences between monopoles, dipoles, quadrupoles and octopoles. The pdf talks about just the multipole expansion of charge distribution only, right? Is the graphical idea of current distribution similar/the same? Also, electric dipole moments, magnetic dipole moments and charge dipole moments are all different, right? Besides charge, electric and magnetic, are there any other sorts of dipole moments?blue_leaf77 said:This subject might be more of a physics subject rather than chemistry. First of all, it's important to realize that there are in general two groups of multipole expansion: multipole expansion of charge distribution and multipole expansion of current distribution. To go further you must go through the related chapter which I don't really recommend if you are only interested in the practical aspect of it. Anyway, I hope this link http://www.pas.rochester.edu/~dmw/phy217/Lectures/Lect_20b.pdf can give you a more graphical picture about multipole expansion for charge distribution, especially in the first slide bottom part where there are 4 different charge configuration. The left most one is the so-called monopole, as we go to the right: dipole, quadrupole, and octopole. They are just the first 4 of infinite number of expansion terms, however as we go to higher terms, the contribution to the expanded quantity (e.g. electric potential) will usually die down and we can simply take the first few terms.
The same goes for current distribution which will generate magnetic multipole expansion. Likewise there are also monopole, dipole, quadrupole terms and so on, however it had been shown that the monopole term for magnetic expansion is always zero, leaving the dipole term to be the most important term in the expansion.
As you see there are electric dipole moment and magnetic dipole moment, but sometimes the first word is dropped and is assumed to be known form the context being discussed.
The dipole moment mentioned in this context must be the electric dipole moment. But of course one can also calculate the magnetic dipole moment of an atom or molecule.
Yes it does.Priyadarshini said:The pdf talks about just the multipole expansion of charge distribution only, right?
Up to now I have never seen the graphical representation of different magnetic multipole expansion, I guess because it's too difficult to put it into drawing.Priyadarshini said:Is the graphical idea of current distribution similar/the same?
The electric dipole is equivalent to the charge dipole, while magnetic dipole to the current dipole.Priyadarshini said:Also, electric dipole moments, magnetic dipole moments and charge dipole moments are all different, right?
Gravitational field due to arbitrary mass density can also be described by multipole expansion, I guess it's something you would call mass multipole expansion.Priyadarshini said:Besides charge, electric and magnetic, are there any other sorts of dipole moments?
Thank you for your help! :)blue_leaf77 said:Yes it does.
Up to now I have never seen the graphical representation of different magnetic multipole expansion, I guess because it's too difficult to put it into drawing.
The electric dipole is equivalent to the charge dipole, while magnetic dipole to the current dipole.
Gravitational field due to arbitrary mass density can also be described by multipole expansion, I guess it's something you would call mass multipole expansion.