# In an inductor, where does the mass increase?
**URL:** https://boards.straightdope.com/t/in-an-inductor-where-does-the-mass-increase/514785
**Category:** Factual Questions
**Created:** [October 22, 2009, 9:45pm UTC](https://boards.straightdope.com/t/in-an-inductor-where-does-the-mass-increase/514785 "2009-10-22T21:45:22Z")
**Posts on this page:** 6
**Page:** 2
### Author:  [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)
#### Post date: [October 25, 2009, 2:23pm UTC](https://boards.straightdope.com/t/in-an-inductor-where-does-the-mass-increase/514785/21 "2009-10-25T14:23:31Z")
> [@JWT\_Kottekoe](#):
>
> The energy density is proportional to the square of the curl of the magnetic vector potential.
Well, that’s the energy of the magnetic field, and you can similarly plug in the equation for **E** to get the electric field energy in terms of **A**. I was wondering if the total electromagnetic field in terms of **A** could be simplified from just the sum of those two terms.
---
### Author:  [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)
#### Post date: [October 25, 2009, 3:54pm UTC](https://boards.straightdope.com/t/in-an-inductor-where-does-the-mass-increase/514785/22 "2009-10-25T15:54:38Z")
> [@Chronos](#):
>
> I don’t know why this always gets trotted out as an example of quantum weirdness, since you can get effects from a field where the field isn’t in classical electromagnetism, too. Consider an ideal solenoid (which produces a magnetic field inside, but little or no magnetic field leakage outside) nested inside another ideal solenoid of larger diameter. If you change the current through the inner solenoid, and thus the magnetic field in it, you’ll produce a current in the wires of the outer solenoid, despite there being no magnetic field at the location of those wires.
When the current in the primary of a transformer changes, the current in the secondary changes because of the existence of the electric force given by Maxwell’s equation, which says that the integral of the electromotive force around a loop is equal to the rate of change of the magnetic flux through the loop. Thus, there is no mystery about something happening in a region with no electric or magnetic fields, since Maxwell’s equations predict an electric force outside the primary. According to quantum mechanics, however, you can measure the flux through the loop (modulo the quantum of flux) even when the magnetic fields are static and no electric or magnetic fields exist outside the primary.
Suppose you wrapped a loop of superconducting wire around a perfectly magnetically shielded solenoid or toroid that is already carrying a current. In classical physics, no current will flow. In quantum mechanics the flowing current will be equal to the mutual inductance times the current in the primary modulo the flux quantum.
The original experiment was done with an electron interferometer. An electron beam was split in two, passed on either side of a magnetic needle, and recombined. The flux through the needle creates a relative phase shift in the wave functions of the two beams. This is observed as a sinusoidal dependence of the intensity of the recombined beams. It is easier and more convincing to do the experiment these days with a commercially available SQUID (superconducting quantum interference device).
There was much controversy after Bohm and Aharanov predicted these effects, but history has shown them to be correct. The effect exists and it cannot be explained by classical physics.
---
### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [October 25, 2009, 10:50pm UTC](https://boards.straightdope.com/t/in-an-inductor-where-does-the-mass-increase/514785/23 "2009-10-25T22:50:44Z")
Yes, the Bohm-Aharanov effect is purely quantum-mechanical, but Faraday’s law is classical, and does have a field producing effects outside of where the field is. If you’re going to just say “That’s OK, because there’s a law of physics that describes that effect”, then you can apply the same reasoning to the B-A effect. My point is that while the B-A effect is an example of a quantum phenomenon, it is not an example of quantum weirdness, since it’s really no weirder than the classical Faraday’s law.
---
### Author:  [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)
#### Post date: [October 26, 2009, 12:45am UTC](https://boards.straightdope.com/t/in-an-inductor-where-does-the-mass-increase/514785/24 "2009-10-26T00:45:43Z")
> [@Chronos](#):
>
> Yes, the Bohm-Aharanov effect is purely quantum-mechanical, but Faraday’s law is classical, and does have a field producing effects outside of where the field is. If you’re going to just say “That’s OK, because there’s a law of physics that describes that effect”, then you can apply the same reasoning to the B-A effect. My point is that while the B-A effect is an example of a quantum phenomenon, it is not an example of quantum weirdness, since it’s really no weirder than the classical Faraday’s law.
In my post, I used the words “curious” and “strange” to describe the Bohm-Aharanov effect. Those adjectives are, of course, subjective and I have no problem if you don’t find them apt. I made no claim that it was, for example, “weird” in the sense of “spooky action at a distance”.
In classical physics it is the fields that matter. They were considered strange when first proposed by Michael Faraday, but were old hat by the time of the invention of quantum theory. For the first 30 years of the theory, I’m not aware that anyone suspected that quantum theory predicted measurable effects in regions that were free of any classical forces. Indeed, when Bohm and Aharanov presented these results, it took some time to convince people. I think I am in good company in the use of these adjectives.
---
### Author:  [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)
#### Post date: [October 26, 2009, 11:22am UTC](https://boards.straightdope.com/t/in-an-inductor-where-does-the-mass-increase/514785/25 "2009-10-26T11:22:31Z")
> [@Chronos](#):
>
> Yes, the Bohm-Aharanov effect is purely quantum-mechanical, but Faraday’s law is classical, and does have a field producing effects outside of where the field is. If you’re going to just say “That’s OK, because there’s a law of physics that describes that effect”, then you can apply the same reasoning to the B-A effect. My point is that while the B-A effect is an example of a quantum phenomenon, it is not an example of quantum weirdness, since it’s really no weirder than the classical Faraday’s law.
I remain unconvinced that there is no electric or magnetic field at the outer solenoid, but still current induced in the outer solenoid when current in the inner one is changed. Why are the electrons in the outer solenoid moving, if not due to an electric field?
---
### Author:  [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)
#### Post date: [October 27, 2009, 1:16am UTC](https://boards.straightdope.com/t/in-an-inductor-where-does-the-mass-increase/514785/26 "2009-10-27T01:16:03Z")
> [@ZenBeam](#):
>
> I remain unconvinced that there is no electric or magnetic field at the outer solenoid, but still current induced in the outer solenoid when current in the inner one is changed. Why are the electrons in the outer solenoid moving, if not due to an electric field?
Perhaps you are correct in your interpretation of Chrono’ last message, but I thought he was agreeing that the effect is due to the electric field outside a solenoid whose magnetic flux is changing. He just doesn’t find it strange that QM predicts a measurable effect in the case of a static field.
[Previous page](https://boards.straightdope.com/t/in-an-inductor-where-does-the-mass-increase/514785.md?page=1)