Electrostatics Question 14
Question 14 - 2024 (30 Jan Shift 2)
A particle of charge ’ $-q$ ’ and mass ’ $m$ ’ moves in a circle of radius ’ $r$ ’ around an infinitely long line charge of linear density ’ $+\lambda$ ‘. Then time period will be given as:
(Consider $\mathrm{k}$ as Coulomb’s constant)
(1) $\mathrm{T}^{2}=\frac{4 \pi^{2} \mathrm{~m}}{2 \mathrm{k} \lambda \mathrm{q}} \mathrm{r}^{3}$
(2) $T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}$
(3) $\mathrm{T}=\frac{1}{2 \pi \mathrm{r}} \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \lambda \mathrm{q}}}$
(4) $\mathrm{T}=\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{m}}}$
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Answer: (2)
$\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{r}}=\mathrm{m} \omega^{2} \mathrm{r}$
$\omega^{2}=\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{mr}^{2}}$
$\left(\frac{2 \pi}{\mathrm{T}}\right)^{2}=\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{mr}^{2}}$
$\mathrm{T}=2 \pi \mathrm{r} \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \lambda \mathrm{q}}}$
