Multipole expansions, calculating the various moments of point charges

milkism
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Homework Statement
Calculate the mono-di and quadrupole moments of the three charges.
Relevant Equations
See solution.
Problem:
a7a1f4ebf284a13000ba8221226cc7b1.png

Solution:
8abe8f08e8a11148085faa3cf6807ad7.png

This was quite simple, are my solutions correct?
 
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Looks very good to me.
 
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Likes PhDeezNutz and milkism
I love your explanations and motivations. Very thorough.
 
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The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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