- #1
davesface
- 97
- 2
Homework Statement
A total charge q is distributed uniformly along a ring of radius b. The ring is in the x-y plane centered on the origin. The multipole expansion is not valid for r<b. Find an expansion for the potential valid in this region
Homework Equations
The charge density is just [tex]\lambda=\frac{q}{2\pi b}[/tex].
The previous problem was about the region r>b, and the book gives the quadrupole-moment tensor components as [tex]Q_{xx}=Q_{yy}=\frac{b^2}{2}q, Q_{zz}=-b^2q, Q_{xy}=Q_{yz}=Q_{xz}=0[/tex] and the potential as [tex]\Phi =\frac{q}{r}+0+\frac{1}{r^5}\frac{b^2q}{4}(x^2+y^2-2z^2)[/tex].
The Attempt at a Solution
Frankly, I don't understand the problem. Obviously at z=0 we can just integrate [tex]\Phi=\int_{0}^{2\pi}\lambda d\theta=\frac{q}{b}[/tex], but that's a pretty trivial introductory level problem. Any thoughts on what exactly this problem is asking me to do?
Last edited: