A steady electric current is flowing through a cylindrical conductor.

Using Ampere’s law, the electric field due to a current carrying conductor of cross section areas is:
magnetic field,
Where,

dl is the current element,

μ₀ is the permeability of free space,

i is the current flowing

R is the radius of the conductor.
At the axis,

R=0 and so no area to enclose current.

Hence, B=0 at the axis of the conductor.

Electric field in the vicinity of the conductor is zero as a minimum distance between the point and the conductor is required to have electric field at that point.
Thus, options (B) and (C) are correct options.