Using the appropriate conversions to Cartesian coordinates, this field can be simulated in a 3D grid. Viewing the X-Y plane at the origin shows the two-lobed field in one plane we expect from a dipole, and it oscillates in time. The image below shows the shape of this field and how the polarity reverses in time due to the cosine term, however it does not currently show the amplitude change due to the time varying strength of the current. Regardless, its shape alone shows the effectiveness of using the electric Hertz vector in this scenario. This approach is significantly more straightforward than finding the electric field in terms of charges within the infinitely thin wire, especially as they vary with time. This is just one of several examples of when the use of Hertz vectors is advantageous compared to more common methods.