# 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? Sep 8, 2018 at 8:16
• homework question?
– jim
Sep 8, 2018 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. Sep 8, 2018 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) Sep 8, 2018 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. Sep 8, 2018 at 9:53

Since the current is constant through the resistor, I can't imagine any reason why the magnetic field strength wouldn't be constant at fixed distance to the resistor either. That's Ampere's Law.

• The current is constant, but the voltage across the resistor is caused by a build up of electrons that cannot all get through the resistor at once. Does such a build up cause a variation in the induced magnetic field in the vicinity of the buildup. I will try to edit the question to clarify why it was asked. Sep 11, 2018 at 3:08
• Build up of elections? I've never heard of such a thing. Sep 11, 2018 at 12:20
• Why wouldn't electrons build up at a barrier restricting their forward movement? Haven't you ever been caught in merging traffic because of a road narrowing or a partial road blockage? Seems illogical that they would not. Sep 11, 2018 at 14:15
• That's not what a resistor does. A resistor prevents a larger amount of current flowing in the first place. You have fewer cars in the first place with a resistor according to Ohm's law, not a backup. Sep 12, 2018 at 15:03
• That is an assumption that I am not saying is wrong: I would just like some proof of that this is the case (as opposed to the build-up of electron concentrations). Hence the original request for a reference to experiments showing a flat-line (option 1) magnetic profile to confirm it to be the case. Sep 14, 2018 at 4:08