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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. enter image description here

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.

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  • $\begingroup$ Assuming $d$ is larger than cross section. What physical law do you use to calculate magnetic field? $\endgroup$ – npojo Sep 8 '18 at 8:16
  • $\begingroup$ homework question? $\endgroup$ – jim Sep 8 '18 at 8:30
  • $\begingroup$ 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. $\endgroup$ – Philip Wood Sep 8 '18 at 8:31
  • $\begingroup$ 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) $\endgroup$ – Excentrix Sep 8 '18 at 8:56
  • $\begingroup$ 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. $\endgroup$ – hdhondt Sep 8 '18 at 9:53
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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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  • $\begingroup$ 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. $\endgroup$ – Excentrix Sep 11 '18 at 3:08
  • $\begingroup$ Build up of elections? I've never heard of such a thing. $\endgroup$ – Trevor Kafka Sep 11 '18 at 12:20
  • $\begingroup$ 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. $\endgroup$ – Excentrix Sep 11 '18 at 14:15
  • $\begingroup$ 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. $\endgroup$ – Trevor Kafka Sep 12 '18 at 15:03
  • $\begingroup$ 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. $\endgroup$ – Excentrix Sep 14 '18 at 4:08

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