1
vote
0answers
60 views

Potential due to a Uniform Ring [closed]

Consider a uniform ring of mass $M$ and radius $a$ (?). I would like to prove that for $r > a$: $$\Phi(r) = \frac{GM}{r} \sum_0^\infty[P_n(0)]^2 \left(\frac{a}{r}\right)^n $$ Where $\Phi(r)$ is ...
3
votes
2answers
138 views

What is the first non-vanishing multipole moment of this configuration?

Imagine that you have a triangle where each side has the length $a$ and a charge $q$ sitting at every vertex. Additionally, we have a charge $-3q$ sitting in the center of the triangle. What is the ...
1
vote
0answers
43 views

Question about “quadrupole radiation” vector potential formula derivation

I tried to get an expression for $\mathbf A (\mathbf x )$ in quadrupole approximation. After some transformations of Liénard–Wiechert vector potential I got, as in many books, $$ \mathbf A \approx ...
0
votes
1answer
557 views

Simple quadrupole moment

I have a very simple problem: There is a charge $-q$ at $(0, 0, d)$ and $(0, 0, -d)$ as well a charge $2q$ at $(0, 0, 0)$. I have to calculate the quadrupole moment using spherical coordinates. I use ...