Magnetic Dipole Moment and Angular momentum

[mer584]

Homework Statement

Show that the magnetic dipole moment M of an electron orbiting a proton nucleus of a hydrogen atom is related to the orbital angular momentum M=(e/2m)L

Homework Equations

M=NIA, Torque =MB, F=qvB=v^2/r, L=Iw=mrv=rp (where p=mv)

N=1 in this case I assume?

The Attempt at a Solution

I've tried every combination of everything I can think of. I started with solving for L as L=2mM/q (where q=e). Then I tried substituting everything I could think of in for L and nothing made sense. I also tried starting with M=Torque/B and substituting I*(angular acceleration) for torque but you just end up with vqr. I think I'm approaching this wrong, can anyone help.

 

[malawi_glenn]

L=Iw

M=NIA

It is not the same I

How is electric current (I in M=NIA) defined?
yes N = 1.

 

[Edward G]

A magnetic dipole is generated by a small current loop (the electron). Try working out the current that the electron generates then crossing that with the area of your little current loop.

Remember:
Current amount of charge per unit time

As you only have one electron, you just have to work out how many times it orbits the nucleus in one second, and multiply it by the electrons charge to get the current.

The dipole is then equal to M = I cross A (I couldn't find the cross symbol) and you can then remove the angular momentum to get the required result.

(This is a little bit of a fudge, but it seems to work)

 

[Ragoza]

What about m? Wouldn't that just give you M=ve/(2*pi*r) * (pi*r²)

 

[klp_l123]

Help me to sort out this problem:: Prove that, "integration over[J(r)dr]=del(p)/del(t)" ... where p is the electric dipole moment ... please as soon as possible, reply me ...