Question

Two identical positive charges Q each are fixed at a distance of 2 a 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. $\sqrt{\frac{4\pi^3ε0rna^3}{q0Q}}$
• B. $\sqrt{\frac{qoQ}{4\pi^3εrna^3}}$
• C. $\sqrt{\frac{2\pi^2ε_0rna^3}{q0Q}}$
• D. $\sqrt{\frac{8\pi^3ε_0rna^3}{q0Q}}$

Answer 1

Answer: (A)

$\sqrt{\frac{4\pi^3ε0rna^3}{q0Q}}$

Answer 2

The correct option is(A): $\sqrt{\frac{4\pi^3ε0rna^3}{q0Q}}$

(x << a) (α is acceleration)

$F_{net}=-(\frac{kq_oQ}{(a-x)}-\frac{kQq_o}{(a+x)^2})$

So, $T=2\pi\sqrt{\frac{4\pi^3ε0rna^3}{q0Q}}$