Dipole moment of the ring
`p=[int_(-pi//2)^(pi//2)(lambda rd theta2r cos theta)]`, where `lambda=(q)/(pi r)`
`=4r^(2)l=(4q r)/(pi)`
From the configuration shown in fig. `vec(tau)=vec(p)xxvec(E )=pE sin theta`
or, `mr^(2)(d^(2)theta)/(dt^(2))=(4 qr)/(mr) E theta`
or `(d^(2)theta)/(dt^(2))=(4 qr)/(mr) E theta` Angular frequency of oscillation is
`omega=sqrt((4qE)/(mr))`
or `T=(2 pi)/(omega)=2pi sqrt((mr)/(4 qE)`