{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

View Full Document Right Arrow Icon
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 .
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern