{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# magenergy - Physics 225/315 February 4 2008 Magnetic...

This preview shows pages 1–2. Sign up to view the full content.

Physics 225/315 February 4, 2008 Magnetic Moments, Energy Levels In SI units the classical magnetic moment of a current loop is μ = IA where A is the area of the loop of radius r and I is the current. Then since the current is the charge divided by the period of the motion μ = ev 2 πr πr 2 = emvr 2 m = eL 2 m = e ¯ h 2 m L ¯ h = μ B L ¯ h where L is angular momentum (= mvr ), μ B is the Bohr Magneton, and ¯ h is Planck’s constant divided by 2 π . μ B = e ¯ h 2 m e = 5 . 8 10 - 5 eV / Tesla = 9 . 27 10 - 24 J / Tesla where e is the magnitude of the electron charge and m e is the electron mass. Check that all the units make sense. 1 eV = 1 . 6 10 =19 J hc = 1240 eV - nm ¯ hc = 200 eV - nm m e 1 / 2 MeV M p 940 MeV We similarly define the Nuclear Magneton using the proton mass. μ N = e ¯ h 2 M P This classical expression can be taken over for the magnetic moment due to the intrinsic angular momentum or spin. M spin = - g s μ B S ¯ h = γS where g s is called the “g factor” and is approximately 2 for electrons. It differs from 2 by about 1 part in 1000. The g factors for protons and neutrons are rather different due to their internal structure. S is the spin angular momentum. For electrons, protons, neutrons, and neutrinos the magnitude of the spin is 1 2 in units of ¯ h . The gyromagnetic ratio γ is γ = - g s μ B ¯ h ≈ - 2 e ¯ h 2 m e ¯ h = - e m e The force on a magnetic moment is an inhomogeous magnetic field is F z = μ z ∂B ∂z The torque on a magnetic moment M in a uniform magnetic field B is M × B .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern