Two charges each of magnitude $Q$ are fixed at $2a$ distance apart. A third charge ($-q$ of mass $'m'$) is placed at the mid point of the two charges; now $-q$ charge is slightly displaced perpendicular to the line joining the charges then find its time period

  • A

    $2\pi \sqrt {\frac{{m{a^3}\pi\, { \in _0}}}{{Qq}}} $

  • B

    $2\pi \sqrt {\frac{{2m{a^3}\pi\, { \in _0}}}{{Qq}}} $

  • C

    $\pi \sqrt {\frac{{m{a^3}\pi\, { \in _0}}}{{Qq}}} $

  • D

    $\pi \sqrt {\frac{{2m{a^3}\pi\, { \in _0}}}{{Qq}}} $

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  • [JEE MAIN 2021]