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: Finding the gyromagnetic ratio of an axially symmetric body

  1. Feb 23, 2014 #1
    1. The problem statement, all variables and given/known data

    So, we can presumably write that m = g L, where L is the angular momentum, g the ratio wanted, and m magnetic dipole moment of an axially symmetric body. Total mass is M, total charge Q, mass density [itex]\rho_m(r)=\frac{M}{Q}\rho_e(r)[/itex], where [itex]\rho_e(r)[/itex] is charge density.

    2. Relevant equations

    Moment of inertia can also be written [itex]I_\omega=\int \rho_m d^2 d\tau[/itex] where d is the distance from the axis of symmetry.

    3. The attempt at a solution

    I guess the dipole moment is in the direction of the axis of the symmetry, as is the angular velocity and it can be written:
    m = g I[itex]_\omega [/itex] ω

    = g ω [itex]\hat{z}[/itex] I[itex]_\omega [/itex]

    m = I [itex] \int d\vec{a} [/itex]

    Here is where I guess I'm having conceptual problems. I is the total current, part of which should be a current flowing through a differential circular loop inside the body, at distance d, that is to say:

    I = [itex]\int \left| v \right| \rho_e d\tau [/itex] , where [itex]\left|v\right|[/itex] is the module of radial speed of a differential volume element (at distance d) that can be written: [itex]\left|v\right|=\left|\omega\right|\left|r\right|[/itex]sin[itex]\theta [/itex]= ωd. [itex] \int d\vec{a} [/itex] of a differential loop in question is simply [itex] d^2 \pi[/itex]. So, im getting:

    g ω [itex]\int \rho_m d^2 d\tau[/itex] =ω [itex]\int d^3 \pi \frac{M}{Q} \rho_m d\tau [/itex]

    Where did I go wrong, how to find g?
  2. jcsd
  3. Feb 24, 2014 #2
    anyone? :( the integrals are supposed to annihilate each other leaving me with a factor ~M/Q
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted