What shape does the Induced Electric Field Lines take when in a region there is Non-Cylindrical Time-Varying Magnetic Field?

Everywhere in the literature I have across, I find that whenever the discussion of the Induced electric field comes, it is discussed around a cylindrical time-varying magnetic field. The induced electric field turns out to be circular in this case.

My question is, what shape does the induced electric field take when the magnetic field is time-varying but non-cylindrical?

Electric and magnetic field around a coil of a rectangular cross-section. Figure 1 shows the geometry of the coil, the distribution of current (red) and magnetic field (blue).

Figure 1.

In fig. 2 shows the distribution of the magnetic field in various sections y=0,0.2,0.4,0.6,0.8,1y=0,0.2,0.4,0.6,0.8,1

Figure 2.

In fig. 3 shows the distribution of the electric field in various sections z=0,0.2,0.4,0.6,0.8,1z=0,0.2,0.4,0.6,0.8,1.It is seen that when moving away from the center of the coil, the lines of the electric field become circular.

Figure 3.

In summary, the Induced Electric Field Lines near the square-shaped coil will be square-shaped near the coil and as we move away from the coil, the shape of these field lines will become circular.

I posted this question on Physics Stack Exchange and received the above response from Alex Trounev (works as a senior AI researcher at Likalo, LLC. He is one of the top 2% of the researchers in the world on Physics Stack Exchange).

The whole conversation can be found here.