An electric dipole has a fixed dipole moment `vecp`, which makes angle `theta` with respect to x-axis. When subjected to a electric field `vecE_(1)=Ehati`, it experiences a torque `vecT_(1)=tauhatk`. When subjected to another electric field `vecE_(2)=sqrt(3)E_(1)hatj` it experiences a torque `vecT_(2)=-vecT_(1)`. the angle `theta` is:

Options

A. `45^(@)`
B. `60^(@)`
C. `90^(@)`
D. `30^(@)`

Answer

B

Explanation

Torque applied on a dipole `t=pE sin theta` where, `theta` angle between axis of dipole and electric field. For electric field `E_1=E hat i`
It means field is directed along positive X direction, so angle between dipole and field will remain `theta` therefore torque in this direction
`t_1=pE_1 sin theta` In electric field `E_2=sqrt3E hat j`
It means field is directed along positive Y-axis, so angle between dipole and field will be
Torque in this direction `t_2=pE sin(90^@- theta)`
`=sqrt3 E_1 cos theta`
According to question `t_2=- vec T_1 implies |t_2|=|t_1| therefore pE _1 sin theta =p sqrt3 E_1 cos theta`
`tan theta=sqrt3 implies tan theta= tan60^@ therefore theta =60^@`