Charge distribution in a current carrying wire

Question

There is a channel on youtube called Electroboom, who has a video titled How Right IS Veritasium?! Don't Electrons Push Each Other?? related to the surface charge distribution in a current carrying wire, where he told that the charge charge density near the terminals of the battery or source is greater than the charge density present in the middle of that loop. The part of the video discussing this starts at 12:54.

So I am here to ask that if the charge density is greater In that region that means the electric field should be present near that region, but it looks it's not.

Answer 1

In the paper A semiquantitative treatment of surface charges in DC circuits (R Muller. Am. J. Phys. 80 (9), Sep. 2012) you can see in Figure 7 that the charge density is indeed higher right next to the terminals of the battery than it is in the middle of the loop.

However, it also shows that there are high charge densities at corners and even along relatively straight portions of the wire depending on the orientation of the wire with respect to the external field. Similar features are also shown in subsequent figures which indicate that this behavior of the surface charges is typical of many different geometrical configurations.

The paper and the figure also show the E field. The E field is rather uniform in magnitude within the conductor, as is expected due to Ohm's law. This is regardless of the external field which varies substantially with distance from the power source.