The current in a DC circuit is associated with the alignment and movement of electrons. At a resistor the free movement of electrons is inhibited, and there is a build up of electrons that creates a voltage across the resistor. The electrons move through the resistor at a rate corresponding to the circuit current, as shown for the simple 2 resistor diagram below.
If there is a build-up of electrons in the areas as shown by the blue ellipses then I would expect that they would effect the strength of the induced magnetic field in their vicinity.
I have been looking for but cannot find what the strength profile of the induced magnetic field profile at a fixed distance $d$ from the center of the wire conductor and across a resistor (assuming both wire and resistor to have the same cross-sectional area, and thus thin or thick film resistors and such like could not be used) around a DC circuit. To eliminate conjectural theoretical arguments, I would really prefer direct measurements from an appropriate lab experiment.
increasing at resistor boundary and reduced across resistor (maroon); and
reduced across the resistor (green).
Possibly it would look like option 4 (i.e. something different to any of the ones shown).
A description of what the profile looks like and an explanation of why would be appreciated. A reference link to an experiment verifying the profile would be fantastic.
Thank you in advance.