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For one of my projects, I've designed the following component to deliver power to loads/circuits:

enter image description here

Fig.1

The component in (Fig.1) breaks into 3 parts(a,b,c), my initial analysis of the current flow is shown in the diagram as (I), however, my concern is with the current flow from component a to b.

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Fig.2

How does the current flow in that region? enter image description here

Fig.3

I tried to break down 3 possible current directions on that edge, which one would be most accurate to describe the current's flow?

The reason I am analyzing that segment, is because of the possible magnetic field associated from this component.

What makes sense to me is a magnetic field that literary wraps around the component, however, a field produced by the sub-current (1) in Fig.3 seems unlikely.

Update:

  • FEA simulation via ANSYS Maxwell:

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Fig.4

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Fig.5

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  • \$\begingroup\$ The conduction band charges will have a nearly completely uniform distribution in the metal shape. There will be a slight excess at the surface, but otherwise very nearly uniform distribution throughout. All the way to the corners. A very, very small number of charges will "stick" at some corners in order to accelerate the charges around the bends. Like negative-gravity, so to speak. (Charges don't turn without a reason.) Plus the needed charge gradient along its length. Can you now work out the drift velocity implications given the shape? What happens if the current increases a lot? \$\endgroup\$ – jonk Nov 25 '17 at 20:58
  • \$\begingroup\$ I will attempt to. A uniform distribution is what I intentionally thought so as well.However, consider my point of confusion: The driving force for the charges is perpendicular to the sub-current(1) in Fig.3, how can current be driven to that region with no driving force towards the corners? Maybe that's my limitation in understanding current flow. \$\endgroup\$ – Pupil Nov 25 '17 at 21:02
  • \$\begingroup\$ There is a very slight charge gradient along the length in order to accelerate the charges, as well. You can actually detect this if you set up a high voltage DC supply and a long wire. Use a pith ball. In the center, the pith ball does nothing. But at each end it is attracted and then instantly repelled as it accumulates some of those charges (which are immediately replaced, of course.) \$\endgroup\$ – jonk Nov 25 '17 at 21:04
  • \$\begingroup\$ I think that there is a big missunderstanding in the intepretation of your question about the scale of your geometry. What are the order of magnitude of the involved variables: nm,um,mm,meters ? Concerning the currents : fA,uA,mA,A,kA ? Do you care about noise under nA ? Personnaly I think that you deal with electrotechnics. \$\endgroup\$ – andre314 Nov 26 '17 at 10:38
  • \$\begingroup\$ Andre, the magnitude should be the standard, A and m. What noise? \$\endgroup\$ – Pupil Dec 3 '17 at 20:25
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This is the kind of thing you solve with finite element analysis.

Basically, you model the region of interest as a mesh of lots of small parts. Then each little part follows the laws of physics, but you can make simplifying assumptions, like that the current is uniform over the small volume. After running enough relaxation iterations, you get the current into and out of the faces of each little element. From that you find the macro current.

There are a lot of details about doing finite element analysis correctly and efficiently, but those are the basic principles. Surely there is software out there already that will do most of this for you.

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  • \$\begingroup\$ Yes, I can use Ansys for this. \$\endgroup\$ – Pupil Nov 25 '17 at 21:21
  • \$\begingroup\$ The problem with FEM here is that the charges have very long range effects in a conductor. FEM is great for statics and heat flow and the like where the entire system can be solved solely by using fine gained locality. But the reality here also requires effects that bridge well beyond a nearby cell. I'd be curious how to correctly set this up in FEM. (I suspect it can be, but it seems nontrivial.) \$\endgroup\$ – jonk Nov 25 '17 at 21:32
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    \$\begingroup\$ @jonk: No, charges don't have any long-range effects in a normal conductor (not semi-conductor). Current in equals current out. No charges build up. You basically only model voltage, resistivity, and current. The solution should be the same as for heat flow assuming the outside of the conductor is perfectly insulated. \$\endgroup\$ – Olin Lathrop Nov 25 '17 at 21:39
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    \$\begingroup\$ Also, Matter & Interactions, 3rd edition, covers some details about the long range effects of just a few charges in corners over many amps of current around a bend. These are long range effects. Any method applied must correctly compute surface charges, gradients, and distributions all on the surface. I suspect it can be done with FEM. Just not the way you suggest. I'm very interested in the detailed setup required to make it yield the right results, quantitatively. \$\endgroup\$ – jonk Nov 25 '17 at 21:47
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    \$\begingroup\$ @andre Writing from phone now. When I can, I'll provide better references. I should be able to find the pages when I get back. The reason I remember them is because they made physical sense and stuck. All physics is local, except at the quantum level, so FEM should work. The problem is in selecting the right view to apply, I think. Which is why things are curious to me. And none of this disagrees with the lack of shot noise in wires being due to long range effects in wires. I think the OP asks an interesting question I'd like to understand and be able to predict, myself. \$\endgroup\$ – jonk Nov 25 '17 at 22:30

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