Two identical dipoles of dipole moment  $\overrightarrow{P}=p_0\widehat{i}$   ( $p_0$  is a positive constant) are placed on x-axis at points   $\text{A}(\text{a},0,0)\text{ and B}(–\text{a},0,0)$as shown. Then pick up the correct statements.

Potential at each point on y-z plane is zero

The electric field at each point on y-z plane (except at infinity) must be perpendicular to y-z plane.

There is a circle of finite radius on y-z plane with centre at origin such that both electric field and potential are zero at each point on its periphery.

If electric field exists at a point on y-z plane, it must be perpendicular to y-z plane.