I was wondering if the $n=2$ term in the potential of a multipole:

$V(r)= \dfrac{1}{4 \pi \epsilon_0} \sum \dfrac{1}{r^{(n+1)}} \int (r')^n P_n(cos \alpha) \rho(r')dv'$

was the same as this equation:

$ V_Q(r) = \dfrac{1}{8 \pi \epsilon_0} \sum_i \sum_j \dfrac{jk}{r^5} Q_{jk} $

where $ Q_{jk} = \int (3j'k'- \delta_{jk}r'^2) \rho(r') dv' $.


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