A dipole of Dipole moment `vec(p)=(p_(0))/(sqrt(2))(hat(i)+hat(j))`. Is placed at origin. Now a uniform external electrical filed at magnitude `E_(0)` is applied along direction of dipole. Two points A and B are lying on a equipotential surface of radius R centered at origin. A is along axial position of dipole and B is along equatorial position. There correct option are :

Options

A. The magnitude of total electric field on any two points of the circle will be same.
B. Total electric field at point A is `vec(E) A = sqrt(2)E_(0) (hat(i) + hat(j))`
C. `R = ((p_(0))/(4 pi epsi_(0) E_(0))^(1//3))`
D. Total electric field at point B is `vec(E)` B =0

Answer

C, D

Explanation

As it is an equipotential surface, E will be perpendicular to the surface, i.e. it is radially outwards.
`V_(0)=0` volts `rArrv_(B)=0` volts [due to dipole = 0, due to `E_(o)` = 0] `rArrV_(A)=V_(B)=0`
`V_(A)=(K_(p))/(R^(2))-E_(0)R=0rArrE_(0)R=(K_(p))/(R^(2))rArr=((K_(p))/(E_(0)))^(1/3)`
`abs(barEA)=(2Kp)/(R^(3))+E_(0)=(2Kp)/(R^(2))xx1/R+E_(0)=(2E_(0)R)/R+E_(0)=3E_(0)rArrbarEA=3/(sqrt2)E_(0)(hati+hatj)`
`abs(barEB)=(-kp)/(R^(3))+E_(0)=-E_(0)+E_(0)=0` Correct options are (CD)