= Spherical current-dipole logarithmic kernel
{title2=$\phi=\frac1b\log\frac{r+P+b}{r+P-b},\quad b=|\mathbf r_0|$}
For $r>b$ and $P=|\mathbf r-\mathbf r_0|$, the displayed kernel satisfies $\phi=\int_r^\infty ds/[s|s\widehat{\mathbf r}-\mathbf r_0|]$. The limit at $b=0$ is $1/r$. Differentiating along $\mathbf Q\times\mathbf r_0$, which preserves $b$, gives $(\mathbf Q\times\mathbf r_0)\cdot\nabla_{\mathbf r_0}\phi=(\mathbf Q\times\mathbf r_0)\cdot\mathbf r/F$. Thus it generates the normalized <magnetic scalar potential> in the <Sarvas formula>.
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