When calculating the Lorentz force of a wire the formula used is:
$$ F = IL \times B$$
I'm curious about the distribution of current($I$) in correlation to the magnitude of the force ($F_L$).
If I applied direct current to a wire and placed it near a magnet, there is a force.
The diagram above is a top view of an example.
The magnet and it's field, and the wire(current going out the page). I learned that with the case of DC, I can assume the current is distributed evenly. However,I'm confused about the nature of how this works... Does that mean that $I$ is the same value at points a,b,c or any point arbitrary point in the conductor? I know that the magnetic field isn't since it weakens with the increase of $r$.
It's a bit counter intuitive for me, to imagine how $1A$ is the value of $I$ in all points.