Two identical positive charges Q each are fixed at a distance of '2a'… | JEE Main 2022 (27 Jul, Shift 1)

Q23JEE Main 2022 · 27 JUL · SHIFT 1Medium

Motion of Charges in an Electric Field

Two identical positive charges $Q$ each are fixed at a distance of '2a' apart from each other. Another point charge $q_0$ 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 $\text{SHM}$ . The time period of oscillation of charge $q_0$ will be:

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Answer: (a)

Displace $q_0$ by $x$ towards one charge: $F = kQq_0\left[\frac{1}{(a+x)^2} - \frac{1}{(a-x)^2}\right] \approx -\frac{4kQq_0}{a^3}x$
$\omega^2 = \frac{4kQq_0}{ma^3} = \frac{Qq_0}{\pi\varepsilon_0 m a^3}$
$T = 2\pi\sqrt{\frac{\pi\varepsilon_0 m a^3}{q_0 Q}} = \sqrt{\frac{4\pi^3\varepsilon_0 m a^3}{q_0 Q}}$
So the answer is (a).

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Motion of Charges in an Electric Field question from JEE Main 2022 (27 Jul, Shift 1)

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