Question:
Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance $x(x< $(\mathrm{m}=$ mass of charged particle $)$
Correct Option: 1
Solution:
Restoring force on proton :-
$F_{r}=\frac{2 K q^{2} y}{\left[d^{2}+y^{2}\right]^{\frac{3}{2}}}$
$Y<< $F_{r}=\frac{2 k q^{2} y}{d^{3}}=\frac{q^{2} y}{2 \pi \varepsilon_{0} d^{3}}=k y$ $\mathrm{K}=\frac{\mathrm{q}^{2}}{2 \pi \varepsilon_{0} \mathrm{~d}^{3}}$ Angular Frequency $: \omega=\sqrt{\frac{k}{m}}$ $\omega=\sqrt{\frac{q^{2}}{2 \pi \varepsilon_{0} m u^{3}}}$