# Magnetic moment?

Hi,

In one part in my book they define the magnetic moment of a closed loop of current. They define it as
$$\overline{\mu} = I\overline{A}$$
with I the current in the loop and $$\overline{A}$$ a vector of magnitude the area of the circuit and perpendicular to the current.

First I thaught it wasn't really important but then they used it again to calculate the magnetic moment of an atom. So it is important after all.

My question is: what does it represent physically? What does it change for a loop or atom to have a higher or lower magnetic moment? I have difficulties grasping the concept.

Thank you.

My question is: what does it represent physically? What does it change for a loop or atom to have a higher or lower magnetic moment? I have difficulties grasping the concept.
Actually it physically represents exactly that, a current carrying loop! If the size of the loop changes then that will give a change in the magnetic moment. If the current changes then that will also give rise to a change in the magnetic moment too.

I am a bit confused regarding the way you phrased your question. What exactly are you asking for when you asked "What does it change for a loop..."?? I may have misunderstood yor question. In any case I'm not sure where you difficulty lies. What about this definition bothers you? Is it the usefulness of such a definition that you're wondering about?

Pete

Hi,

I'm sorry if I didn't explain my question well. What I want to ask is, why in the world would they want to define the magnetic moment $$\overline{\mu} = I\overline{A}$$. How is it useful? It's direction doesn't give any information (as $$\overline{A}$$ as a vector is only defined on a closed surface) and I don't see what information its magnitude gives...

I hope you understand my problem?

Hi,

I'm sorry if I didn't explain my question well. What I want to ask is, why in the world would they want to define the magnetic moment $$\overline{\mu} = I\overline{A}$$. How is it useful? It's direction doesn't give any information (as $$\overline{A}$$ as a vector is only defined on a closed surface) and I don't see what information its magnitude gives...
I hope you understand my problem?
"They" don't define the magnetic moment that way. We calculate from first principles that the magnetic moment of a current loop is $$I{\bf A}$$.
$$\overline{A}$$ as a vector is only defined on an open surface like that of a loop.
I am afraid I don't understand your problem.

Ok I'm sorry I'll try to make it clear now :-).

"Now we define the linear momentum to be $$\overline{p}=m\overline{v}$$."
When I read further, it occured to me that the definition of linear momentum has a lot of useful properties: elastic/not elastic, conservation of linear momentum,...

Now what "useful" properties does the magnetic moment have? Does it make calculations more easy? Does it represent something physically?

All it matters is how the magnetic momentum interacts with the rest of the world, particularly:

a) how do you use the momentum to figure out how your object is affected by a magnetic field
b) how do you use the momentum to figure out how your objects affects something else

The particular definition as a product current x area represents originally the special case of an electric circuit (a "spire" = a wire loop with current flowing in it).

However you can also use the idea of a spire to interpret a large array of situations where you don't really have a wire, as is the case with a single electron orbiting: you can picture a "ghost spire" where the current is made by the electron itself looping its orbit, and the area is outlined by the electron's trajectory. The same idea is used a lot in electromagnetism, for example to see a permanently magnetized piece of iron as having loops of currents flowing on its surface (like it was a pile of spires).

Ok I'm sorry I'll try to make it clear now :-).

"Now we define the linear momentum to be $$\overline{p}=m\overline{v}$$."
When I read further, it occured to me that the definition of linear momentum has a lot of useful properties: elastic/not elastic, conservation of linear momentum,...

Now what "useful" properties does the magnetic moment have? Does it make calculations more easy? Does it represent something physically?
Having defined $$\mu$$ as the magnetic dipole moment of a current loop as having magnitude NiA and direction as per a RHR, we can then define the torque exerted by an ext mag field as $$\tau=\mu\times$$$$B$$ and the dipole's magnetic potential energy as U= -$$\mu\cdot$$$$B$$.
These equations can be used for torque/energy/work problems involving any current loops. For example current carrying coils, simple bar magnets, a rotating sphere of charge. Also most subatomic particles, including the electron, proton and neutron have magnetic diploe moments, and so the concept is also used in quantum physics.
There are corresponding equations for electric dipole moments too.
Hope this helps.

Ok thank you for the both of you. It's clearer now for me :-).