Alexandr A.Shpilman ( alexandrshpilman78@gmail.com )
How does electric current flow in a conductor?
It is well known, but not advertised, that a direct electric current in a conductor does not flow in a continuous stream. If we try to show what it looks like in the cross section of conductor 1, we will have many “jets” 2 of current of electric charges in the conductor.
Why this is so, no explanation is given.
Let's consider a picture of the magnitude of the magnetic vector potential A (3) between two long, parallel electrical conductors 1 and 2 with an electric current flowing through them in one direction.
The magnitude of the magnetic vector potential 3 is equal to:
|
|
A(x) ~ j* (1+ln(a/(a+x)) + ln(b/(b-x))) |
(1) |
|
where |
j – the magnitude of the electric current in the “jet” |
Formulas from quantum mechanics:
|
|
P(x)=P0-SQRT(q*U(x)*m)– q *A(x)/c |
(2) |
|
where |
P0 – initial electron momentum; |
Change in the impulse of an electric charge carrier in a “jet” of electric current:
|
|
p(x) ~ – q*A(x)/c |
(3) |
Change in the speed of an electric charge carrier in a “jet” of electric current:
|
|
v(x) ~ – q*A(x)/(m*c) |
(4) |
Those. the speed of electric charges in the “jet” decreases. For electric charges moving in the vector potential, an electric field also appears:
|
|
E(x) ~ – grad(A(x)) |
(5) |
Which will pull free electric charges in the conductor into the resulting “jets” of electric current. Until this field exceeds the electric field from an increase in the charge density in the “jet”.
It must be assumed that this kind of instability in the flow of electric current will manifest itself in both superconductors and electrolytes.
It is worth recalling that free electric charges in metals are not free in reality. See Foucault currents. So in reality the situation is more complex and the figures often given in articles for the speed of flow of electric charges in a conductor are incorrect.