It may seem like a stupid question. I'm new to pcb design. I designed a trace similare to the following picture (Excuse me for poor graphics)
My PCB trace is like the left picture, now when current flows how do electrons flow? I'm a mechanical engineer so I imagine it should be something like flow of a fluid as I've shown on the right picture. If it's so the sharp corners do nothing! Can somebody please explain that to me?
I found this question very interesting, so I did a SPICE simulation. (Sorry for not using the design tool of this site, but I needed a bit more control over the simulation...)
I placed 6146 resistors of 1 Ohm horizontally and vertically on a grid, as shown below. (The red part is shown magnified in the middle)
At the bottom, there's a 1V voltage source connected to the lower ends of the vertical bars.
The SPICE simulation calculates the voltage at each node, and the voltage distribution looks like this:
To see more details, I used a rotating HSV color scheme where colors are repeated. The voltage difference between two neighboring areas of same color is 50mV. The faster the colors change, the higher the voltage gradient and so the current is.
From the voltage distribution one can calculate the current flowing out of each node into the connected resistors:
From this picture, it's already clear that there is a higher current density at the "inner" corners and a lower current at the "outer" corners. However, to see more details, I once again used the other color scheme, where the current difference between two neighboring areas of same color is 4mA.
If we have a look at the current profile along the dotted lines in the plot above, we get this:
While the current is more or less constant (~3.5mA) over the entire width of the track along the horizontal and vertical line, it is almost three times as high at the inner upper right corner and falls to almost zero to the outer corner.
Electrons are very very tiny, \$2.8^{-15}m\$.
Why would you think at that scale, a sharp corner is different from any edge of a conductor? Electrons would only 'notice' an edge when they get quite close, hence an edge and a corner wouldn't have much of a different effect until it gets very close, and that can only apply to a tiny number of electrons. Also, at these scales, the edge of the track is going to 'look' as much like a corner as an actual corner.
There will be some electrostatic forces at corners, so a corner will do something, but I SWAG only within a few electron diameters of the track edge, and so a corner is not going to be very significantly different to a track edge to the fast majority of electrons (until you get to very high frequencies).
The speed of propagation of a signal (a significant fraction of c, the speed of light) isn't related to the speed of movement of electrons.
Electrons move quite slowly, for example this wikipedia article Electron Drift velocity estimates drift velocity at 0.00028 m/s (under 1mm/second).
So an electron isn't going to 'do a road runner' and 'fly off the cliff-road' trying to go round a corner, or or have to 'put the brakes on' going into the corner.
Similar to the flow of a fluid the flow of an electrical current can be "impeded" by some obstacles. In the case of your diagram, there is some small increase in electrical impedance at the sharp corners. The impeding force is from the induced fields that are generated around any conductor that carries an electrical current. For a rough visualization you can draw concentric rings centered on the assumed current path in your diagram. (The rings simulate the magnetic field lines.) In the conductor areas with dense or crossing rings there is increased impedance to the direction of flow. Even for a simple straight line trace some of the field lines will pass through the conducting material and give some impedance. Additional issues can arise when multiple signal carrying traces come close on a PCB. The field lines from one trace can interfere or impede signals on the other trace.
All this may sound like you need to create smooth curved traces for all your circuits. Actually, except for the most critical cases this is usually not necessary, and not all PCB drawing systems even provide this option. As a compromise it is often helpful to try to avoid or reduce the number of 90 deg bends, (use two 45 deg bends instead), this practice is more helpful only for highest frequency traces. Traces with only low frequency or DC currents benefit much less by reducing sharp corners. Overall reducing 90 deg bends can still be beneficial for reducing board space and minimizing PCB manufacture issues.
As a more basic idea, the electrical current flow takes the path of least resistance (and any "impedance" to the flow can be thought of as a resistance). When getting more precise, (and with higher frequency circuits) you would treat the impedance values and resistance values separately.
If you really need to know, the electrons actually flow from the negative connection (GND in this case) to the positive connection. This may seem backwards but this is only due to the fact that electrons are defined as being negatively charged entities, (dare I say particles).
If you really want to think about it in mechanical terms, the flow of electrons in a conductor is much more like a compressible gas than an incompressible fluid like water.
A gas will fill all of the available space regardless of pressure, just as electrons will "fill" all of the volume of the conductive copper.
A wider trace (equivalent to a wider pipe) will always have less resistance to flow, regardless of the size of the terminal connection.
Current will actually will flow in all sections of the trace in your drawing, although current density will be higher in the black region you overlaid -- especially around the corners. Removing any of the trace would increase the total resistance between the nodes, although removing the outer corners would make a very small change. Filleting the inner corners might make a useful improvement.
Generally for calculating the resistance of this type of structure, it is sufficiently accurate to count squares -- for a given material resistivity, the resistance of a square of trace (equal length and width) is a fixed value. Count squares down the middle of the trace, and allow 1/2 for a corner.
This isn't 100 % accurate -- corners are actually closer to 0.4 * square resistance when connected by 'long' traces; with tighter shapes like you have here (length of trace between corners is not >> width), the calculation is more complex.
