1. Electric Charges and Fields
hard

Two identical positive charges $Q$ each are fixed at a distance of ' $2 a$ ' apart from each other. Another point charge qo with mass ' $m$ ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_{0}$ executes $SHM$. The time period of oscillation of charge $q_{0}$ will be.

A

$\sqrt{\frac{4 \pi^{3} \varepsilon_{0} m a^{3}}{q_{0} Q}}$

B

$\sqrt{\frac{q_{0} Q}{4 \pi^{3} \varepsilon_{0} m a^{3}}}$

C

$\sqrt{\frac{2 \pi^{2} \varepsilon_{0} m a^{3}}{q_{0} Q}}$

D

$\sqrt{\frac{8 \pi^{3} \varepsilon_{0} m \alpha^{3}}{q_{0} Q}}$

(JEE MAIN-2022)

Solution

$m \operatorname{acc}^{ n }=\frac{ KQq _{0}[2 a ][2 x ]}{\left( a ^{2}- x ^{2}\right)^{2}}$

$\Rightarrow \operatorname{acc}^{ n } \approx\left(\frac{4 kQq _{0}}{ ma ^{3}}\right) x$

$T =2 \pi \sqrt{\frac{\pi \varepsilon_{0} ma ^{3}}{ Qq _{0}}}$

$T =\sqrt{\frac{4 \pi^{3} \varepsilon_{0} ma ^{3}}{ Qq _{0}}}$

Standard 12
Physics

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