- #1
snatchingthepi
- 148
- 38
- Homework Statement
- Finding the vector potential inside and outside of a rotating homogenous solid sphere.
- Relevant Equations
- ## r_< = min(r,r') ##
##r_> = max(r,r') ##
I'm trying to solve the vector potential of a solid rotating sphere with a constant charge density. I'm at a point where I'm performing the final integral that looks like
$$ -\left( \frac {\mu_0 i} {3} \right) \sqrt{\frac 3 {2\pi}} \frac {q\omega}{R^3} Y_{1,1} \int_0^R (r')^3 \frac {r_<} {r_>^2} dr'$$I'm thinking that outside the sphere ##r_> = r## and ##r_< = r'##, and vice-versa for inside the sphere. Is this correct? I've never seen those functions before, and am unsure if I'm interpretating them correctly.
$$ -\left( \frac {\mu_0 i} {3} \right) \sqrt{\frac 3 {2\pi}} \frac {q\omega}{R^3} Y_{1,1} \int_0^R (r')^3 \frac {r_<} {r_>^2} dr'$$I'm thinking that outside the sphere ##r_> = r## and ##r_< = r'##, and vice-versa for inside the sphere. Is this correct? I've never seen those functions before, and am unsure if I'm interpretating them correctly.
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