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  • $\begingroup$ I think you forgot to include the absolute values in the second straight-line integral. If $-b < \ell < -a$ then $|\vec{r} - \vec{r}'| = -\ell$, not $\ell$. $\endgroup$ Commented May 30 at 13:38
  • $\begingroup$ @MichaelSeifert Thank you very much! $\endgroup$
    – want2know
    Commented May 30 at 14:14