Near field intensity in terms of antenna thickness
In an EM radiating antenna a proper EM field does not form until beyond the near field: -



On the diagram above proper coherent EM waves are in the far-field. Of course if you could build an antenna that operated at DC the near field would extend to infinity: -



But I doubt that the thickness of the wire has anything to do with it. You have to match the E and H fields to the impedance of free space (377 ohms) to make an EM antenna an effective radiator: -



E and H fields in the near field are neither of the correct ratio nor of the correct phase angle with respect to each other. They decay individually as \$\dfrac{1}{d^3}\$. In the far field they individually decay as \$\dfrac{1}{d}\$

On this basis alone your question contradicts itself because you cannot be referring to a real EM antenna.