Why are there 2 definitions of Magnetic Moment?

[tessx]

Hello everyone, this is my first post at Physics Forums!

I am trying to understand electromagnetism, and when it comes to the magnetic moment, when reading around I see $$\mu = IA$$ where A is area of a loop, which is an expression I can sort of understand. But when reading about magnetic drifts (I am a little confused for the moment) I see $$\mu = \frac{m v^2}{2 B}$$. I am sure both refer to the same value but I cannot visualise how.

Would someone be kind enough to explain this to me?

Thank you!

Tessx

 

[jtbell]

I don't remember ever seeing your second equation. If you found it on the Web, can you give us a link to it, or if in a book, which book it was and what the context of the equation was? (What was the book discussing at that point?)

 

[tessx]

jtbell,

The context of the second equation is in space plasmas, describing the ratio between perpendicular particle energy and magnetic field.
I found the equation in a book called "Basic Space Plasma Physics" by Baumjohann W. and Treumann R. A., Imperial College Press 2004.
What I don't get is how do they get to this expression, and how does it "fit" with the other one (=IA).

Thank you for your help!

 

[jtbell]

Unfortunately, I don't know squat about space plasma physics. Maybe someone who does know something about it will see this.

 

[marcusl]

I'd say that your second equation is a derived equation appropriate to a particular problem. Note that (mv^2)/2 is kinetic energy and mu B has units of energy, so this equation relates the energy of a moment in a field to some situation where particles are moving. It is not a fundamental definition of moment like the first equation.