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2. Electric Potential and Capacitance
hard
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
A
$\sqrt \frac{mr_1r_2Qq}{\pi\varepsilon_0(r_1 +r_2)}$
B
$\sqrt \frac{mr_1r_2Qq}{2\pi\varepsilon_0(r_1 +r_2)}$
C
$\sqrt \frac{mr_1r_2Qq}{3\pi\varepsilon_0(r_1 +r_2)}$
D
$\sqrt \frac{mr_1r_2Qq}{4\pi\varepsilon_0(r_1 +r_2)}$
Solution
$\frac{1}{2} m V_{1}^{2}-\frac{K Q q}{r_{1}}=\frac{1}{2} m V_{2}^{2}-\frac{K Q q}{r_{2}}$
$\mathrm{mV}_{1} \mathrm{r}_{1}=\mathrm{L}_{0}$
$\mathrm{mV}_{2} \mathrm{r}_{2}=\mathrm{L}_{0}$
Solving eqns:
$L=\sqrt{\frac{m r_{1} r_{2} Q q}{2 \pi \varepsilon_{0}\left(r_{1}+r_{2}\right)}}$
Standard 12
Physics
