A particle of mass $m$ having negative charge $q$ move along an ellipse around a fixed positive charge $Q$ so that its maximum and minimum distances from fixed charge are equal to $r_1$ and $r_2$ respectively. The angular momentum $L$ of this particle is
Diffcult
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$\frac{1}{2} m V_{1}^{2}-\frac{K Q q}{r_{1}}=\frac{1}{2} m V_{2}^{2}-\frac{K Q q}{r_{2}}$
$\mathrm{mV}_{1} \mathrm{r}_{1}=\mathrm{L}_{0}$
$\mathrm{mV}_{2} \mathrm{r}_{2}=\mathrm{L}_{0}$
Solving eqns:
$L=\sqrt{\frac{m r_{1} r_{2} Q q}{2 \pi \varepsilon_{0}\left(r_{1}+r_{2}\right)}}$
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