Magnetic Fields - Just Convenient Mathematical Conceptualizations?

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Discussion Overview

The discussion revolves around the conceptualization of magnetic fields in physics, particularly in the context of electromagnetic induction, Lenz's Law, and energy transfer. Participants explore whether magnetic fields are merely convenient mathematical constructs or if they have a more fundamental role in physical phenomena.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant suggests that magnetic fields are convenient conceptualizations that help explain energy transfers, such as the conversion of kinetic energy to heat in eddy currents.
  • Another participant argues against the dismissive use of "just," emphasizing that mathematical conceptualizations are essential in science and should not be belittled.
  • A participant questions why magnetic fields are singled out as mere conceptualizations when electric fields are similarly conceptualized.
  • One reply clarifies that while magnetic fields store energy, they do not necessarily transfer energy, and that they exert forces without doing work on charged particles.
  • Another participant points out that establishing a magnetic field does not inherently involve energy dissipation, citing examples of oscillating magnetic fields in resonators.
  • There is a discussion about the nature of eddy currents and their relation to diamagnetism versus paramagnetism, with some confusion about the role of aluminum as a paramagnetic material.
  • Some participants note that magnetic fields are unique in that they arise from moving charges, contrasting them with electric and gravitational fields, which are associated with stationary charges and mass, respectively.
  • One participant raises a question about the source of energy for establishing a magnetic field around a wire.
  • Another participant argues that the observation of magnetic fields for low-speed charges could be considered a relativistic effect, suggesting that the relationship between electric and magnetic fields is frame-dependent.

Areas of Agreement / Disagreement

The discussion contains multiple competing views and remains unresolved. Participants express differing opinions on the nature and role of magnetic fields, with some supporting the idea of them being mere conceptualizations while others defend their fundamental significance.

Contextual Notes

Participants highlight various assumptions and limitations in their reasoning, such as the distinction between energy storage and energy transfer in magnetic fields, and the specific conditions under which magnetic fields arise. There is also a lack of consensus on the implications of these conceptualizations in relation to physical phenomena.

modulus
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With my term-end examinations fast-approaching, I sat down to revise my entire senior year physics syllabus. As I was reading through electromagnetic induction, I found myself in the same state of utter confusion that I found myself in when I first studied about Lenz's Law and Eddy Currents. But this time, I think I am in a position to better justify the ideas I am developing.

It seems to me that magnetic fields are just convenient conceptualizations, which allow us to account for a number of energy transfers in an elegant manner. For example, when extended metal (para-magnetic) objects enter a magnetic field, they develop eddy currents, which are oriented so as to oppose the motion otherwise. Another example is the force that pulls a current loop back into the magnetic field as it is being pulled out by an external agent.

In both cases, the work done by the external forces that would otherwise show up as kinetic energy, show up as heat (the eddy currents, the induced current). So, essentially, there is just a transfer of energy (from kinetic to heat). But if we want to explain the slowing down of the metal object or the current loop in terms of forces, then magnetic fields 'allow' us to do that. In this sense, they just seem to be convenient (and astonishingly elegant) mathematical vector fields that just 'work'!

What strengthens my resolve in this matter is Joule heating. We say that when a current flows through a resistor, there is heat energy dissipated apparently, the work done by the battery or cell has been converted to thermal energy). But what about the magnetic field the wire sets up? That is supposed to hold energy within it's 'volume', right? Moreover, it does not change with time. Somehow, the heat energy has been converted into a magnetic field, which persists (this is in contrast to what happens in eddy currents, where the result is a 'dispersion' of energy from kinetic to thermal energy, which, as it seems, is entropically favorable).

If I am going on the wrong track here, If there is a serious flaw in my reasoning, someone throw me back on the right track. Because if this is right, then the implications of it are pretty interesting...
 
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Why the pejorative use with "just"? Yes, magnetic fields are mathematic conceptualizations - a grand thing indeed! Dont belittle it with "just", this is how physics and science works. Its all conceptualizations (mathematical or otherwise) that form theories based on observations. The electric field is also a mathematical conceptualization. So is the electric charge, so is the gravitational field, etc.

Dont be dissin' on mathematical conceptualizations as though they are not good enough, they are the best we can do (in science) and can be quite powerful!
 
By your "logic", electric field is also a "convenient mathematical conceptualization". So why pick on magnetic field only?

Zz.
 
I would look to address some of the misconceptions in your post.
1) While a magnetic field stores energy, it may or may not transfer energy. As an example, a magnetic field does no work on a charged particle moving through it. It does exert a force on that particle, however, so thinking of it at a mediator of force is probably more useful (indeed, field lines are often referred to as "lines of force").
2) There need be no heat or dissipation involved in establishing and maintaining a magnetic field. A resonator consisting of an inductor and capacitor in series produces an oscillating magnetic field in the inductor, but there need be no dissipation.
3) Your example of eddy-currents opposing motion in a B field applies to diamagnetism, not paramagnetism.

Hope that's helpful.
 
You can't 'see' any fields. You only know that something happens to charges and masses, when you put them and move them in space. We just describe the effect in terms of fields. Lines of force are only in our heads! You can describe forces in other terms - as in the forces between two point charges or two point masses.
 
3) Your example of eddy-currents opposing motion in a B field applies to diamagnetism, not paramagnetism.

So does that mean that paramgnetic substances do not expeience electromagnetic damping? My textbook gives an example with an aluminum rod...


By your "logic", electric field is also a "convenient mathematical conceptualization". So why pick on magnetic field only?

Yes, in the most fundamental sense. But electric fields are set up by stationary particles, by virtue of an intrinsic property of the particle - the charge. Similarly with gravitational fields (the mass). But magnetic fields are peculiar in the sense that they are set up only when these particles are in a specific state of motion...but obviously, a particle couldn't transform into another particle or takke up a new 'intrinsic property' in some state of motion (and magnetic fields are observed for charges moving at very low speeds as well, so it does not seem to be a relativistic effect).


Also, where does the energy for setting up the magnetic field around the wire come from?
 
Aluminum is paramagnetic, but that is not what causes the retarding force. In fact, paramagnetic materials are pulled in to a field. It is eddy currents at work, as you said, which depend only on the fact that aluminum is an electric conductor.
 
modulus said:
Yes, in the most fundamental sense. But electric fields are set up by stationary particles, by virtue of an intrinsic property of the particle - the charge. Similarly with gravitational fields (the mass). But magnetic fields are peculiar in the sense that they are set up only when these particles are in a specific state of motion...but obviously, a particle couldn't transform into another particle or takke up a new 'intrinsic property' in some state of motion (and magnetic fields are observed for charges moving at very low speeds as well, so it does not seem to be a relativistic effect).

Unless you are claiming that spin magnetic moments are due to a "... Specific state of motion...", then what you mentioned here is false.

Zz.
 
modulus said:
(and magnetic fields are observed for charges moving at very low speeds as well, so it does not seem to be a relativistic effect).
Actually, it can be considered a relativistic effect. What is an E field in one frame is an E field and a B field in another frame. http://physics.weber.edu/schroeder/mrr/MRRtalk.html

Regarding your general point, every physical quantity is a mathematical abstraction in some sense, so it seems weird to single out the B field.
 
  • #10
Actually, it can be considered a relativistic effect. What is an E field in one frame is an E field and a B field in another frame. http://physics.weber.edu/schroeder/mrr/MRRtalk.html

Enlightening...

I barely know anything about quantum physics, so I don't know if I'm talking about spin-only magnetic moments...or what they are (in reply to ZapperZ).

Anyways, thank you.

Yeah...maybe I was pushing it abit...
 

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