Question

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 SHM. The time period of oscillation of charge $q_0$ will be :

• A. $\sqrt{\frac{4{\pi }^3{\epsilon }_{0}m{a}^3}{q_{0}Q}}$
• B. $\sqrt{\frac{q_{0}Q}{4{\pi }^3{\epsilon }_{0}m{a}^3}}$
• C. $\sqrt{\frac{2{\pi }^2{\epsilon }_{0}m{a}^3}{q_{0}Q}}$
• D. $\sqrt{\frac{8{\pi }^3{\epsilon }_{0}m{a}^3}{q_{0}Q}}$

Answer 1

Answer: (A)

$F=macc{}^n=\frac{KQ{q}_0}{(a-x{)}^2}-\frac{KQ{q}_0}{(a+x{)}^2}$
$mac{c}^n=\frac{KQ{q}_0[2a][2x]}{{\left(a^2-x^2\right)}^2}$
$\Rightarrow {\mathrm{acc}}^n\approx \left(\frac{4kQ{q}_0}{m{a}^3}\right)x$
$T=2\pi \sqrt{\frac{\pi {\epsilon }_{0}m{a}^3}{Q{q}_0}}$
$T=\sqrt{\frac{4{\pi }^3{\epsilon }_{0}m{a}^3}{Q{q}_0}}$