An electric dipole with dipole moment $$\frac{p_o}{\sqrt 2} (\widehat{l}\widehat{J})$$ is held fixed at the origin O in the presence of an uniform electric field of magnitude $$E_0$$. If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are:
($$\epsilon_0$$ is permittivity of free space. $$ R \gg$$ dipole size)

A

$$R = \left(\frac{p_0}{4\pi \epsilon_0 E_0}\right)^{\frac{1}{3}}$$

B

Total electric field at point A is $$\overrightarrow{E}_A = \sqrt 2 E_0 (\widehat{l}\widehat{j})$$

C

Total electric field at point B is $$\overrightarrow{E}_B = 0$$

D

The magnitude of total electric field on any two points of the circle will be same.