A dipole has two charges `+1muC " and "-1muC` and each of mass 1 kg. The separation between the charges is 1 m. An electric field `20 times 10^(3)Vm^(-1)` is applied on the dipole. If the dipole is deflected through `2^(@)` from the equilibrium position, then the time taken by it to come to equilibrium position again is

Options

A. `2.5pi`
B. `2pi`
C. `5pi`
D. `4pi`

Answer

A

Explanation

Torque on dipole, when it is deflected by a samall angle `theta is tau =pE sin theta=p E theta`{ for small angle, sin `theta= theta}`
But `tau = I alpha`
Where , `I=mr^2+mr^2=2mr^2`
So, angular acceleration of dipole is `alpha = (p E theta)/(I)`
TIme to align back with field is `( " using theta= 1/2 alpha t^2)`
`t = sqrt((2 theta)/(alpha))=sqr t(2 theta I)/(p E theta )= sqrt((2I)/(PE))= sqrt(50 )~~ 2.5 pi (s)`