The vector potential of a Hertzian dipole falls off spherically as $1/r$. The polar axis of the dipole is a "Null" field -- meaning no electric and magnetic field. The absence of magnetic field is clear enough since there is no curl in the vector potential there. However, the potentials description of the E field involves the equation:
$$\mathbf E = -∇Φ - ∂\mathbf A/∂t$$
which seems to indicate there will be an oscillating electric field in the far field of the Hertzian dipole -- even in the "Null" of the dipole, where the where there should be no electric field.
Clearly, as there is no poynting vector in the "Null", an electron placed there can not oscillate in response to an oscillating electric field as there is no energy locally available, otherwise we'd encounter a violation of conservation of energy or a violation of locality.
How is this conundrum resolved?