What is the magnetic field profile around an electronic resistor?

magnetic-fields electric-current electrical-resistance

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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.

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Excentrix

Updated on June 16, 2022

Comments

Excentrix less than a minute
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.

Thank you in advance.
- npojo almost 4 years
  
  Assuming $d$ is larger than cross section. What physical law do you use to calculate magnetic field?
- jim almost 4 years
  
  homework question?
- Philip Wood almost 4 years
  
  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.
- Excentrix almost 4 years
  
  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)
- hdhondt almost 4 years
  
  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.
- npojo almost 4 years
  
  (1) $\mu$ is relevant to the region and material where you measure the magnetic field, not related to the material of the current carrier. (2) Ampere's law is empirical and maps measured current to magnetic field. A non transient charge built-up, like in a capacitor will probably not cause any magnetic field.
- Excentrix almost 4 years
  
  The resistor would not be a thin or thick film commercial resistor because it should have the same cross-sectional area as the wire conductor. It would need to be a wire with much more resistance than the wire conductor itself.
- Excentrix almost 4 years
  
  True about μ. But the question remains unanswered: with a wire resistance of the same cross-sectional area but much higher resistance than the wire conductor is used, what does that magnetic field profile look like?
Excentrix almost 4 years

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.
Trevor Kafka almost 4 years

Build up of elections? I've never heard of such a thing.
Excentrix almost 4 years

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.
Trevor Kafka almost 4 years

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.
Excentrix almost 4 years

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.