# What is the magnetic field profile around an electronic resistor?

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.

In the sketch below,
$\hspace{150px}$,
I have shown 3 possibilities:

1. constant (blue);

2. increasing at resistor boundary and reduced across resistor (maroon); and

3. 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.

• Assuming $d$ is larger than cross section. What physical law do you use to calculate magnetic field? – npojo Sep 8 '18 at 8:16
• homework question? – jim Sep 8 '18 at 8:30
• You need to take npojo's hint. It might help to idealise the set-up by making the top portion of the circuit (the resistor and horizontal portion of connecting wires) very long compared with $d$, and to also to keep the 'bottom' of the circuit (not shown) a long distance away. – Philip Wood Sep 8 '18 at 8:31
• Ampere's law shows B=µI/2πd. Assuming d to be a reasonable distance (within millimeters) of the wire/resistor does a change in µ between the wire and resistor alter the profile, and/or can a build-up of electrons at the wire/resistor interface change B, or a combination of such factors? (P.S. not a homework problem) – Excentrix Sep 8 '18 at 8:56
• What kind of resistor? A film resistor will have a different field from a wirewound resistor. For a film resistor, remember the current is the same all along the circuit. – hdhondt Sep 8 '18 at 9:53