A dipole of fixed length \( 2R \) consists of two masses \( m \), each located at the ends of the dipole. The dipole has charges \( +Q_2 \) and \( -Q_2 \) on its ends and orbits a fixed point charge \( +Q_1 \). The ends of the dipole are constrained to remain in the orbital plane.
If the dipole is in a circular orbit about \( Q_1 \), with \( r \approx r_0 \) and \( \alpha \ll 1 \), find the period of small oscillations .
1
\( T = 2\pi \sqrt{\frac{4 \pi \epsilon_0 m R r^2 }{Q_1 Q_2}} \)
2
\( T = 2\pi \sqrt{\frac{2 \pi \epsilon_0 m R r^2 }{Q_1 Q_2}} \)
3
\( T = \pi \sqrt{\frac{4 \pi \epsilon_0 m R r^2 }{Q_1 Q_2}} \)
4
\( T = \pi \sqrt{\frac{2 \pi \epsilon_0 m R r^2 }{Q_1 Q_2}} \)