1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Magnetic dipole moment of a sphere

  1. Dec 25, 2006 #1
    1. The problem statement, all variables and given/known data
    Find the magnetic dipole moment of a spherical shell of radiu R carrying a uniform surface charge sigma, set spinning at angular velocity omega.

    2. Relevant equations
    [tex] \vec{m} = \frac{1}{2} \int_{S} \vec{r'} \times \vec{K} (\vec{r'}) da' [/tex]

    3. The attempt at a solution
    So we gotta figure out the surface charge density (since it is a spherical shell)

    [tex] K = \sigma v [/tex]

    and [tex] v = \omega times R [/tex]
    this is where i am doubtful...
    the angle between v and R varies from 0 to 2 pi

    so this cross product is not unique...
    or am i thinking about this the wrong way??

    please help!
  2. jcsd
  3. Dec 26, 2006 #2


    User Avatar
    Science Advisor
    Gold Member

    You are right that the angle changes but v will always point in the correct direction. The changing angle ([tex]sin(\theta)[/tex]) accounts for the "azimuthal radius", that is, distance from the spin axis z to the shell measured parallel to the xy plane, that changes with polar angle. That distance is also the r you need to use in your integral.

    BTW, polar angle only varies from 0 to [tex]\pi[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook