# Magnetic Fields - Just Convenient Mathematical Conceptualizations?

1. Mar 2, 2013

### modulus

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...

2. Mar 2, 2013

### ModusPwnd

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!

3. Mar 2, 2013

### ZapperZ

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

Zz.

4. Mar 2, 2013

### marcusl

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.

5. Mar 2, 2013

### sophiecentaur

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.

6. Mar 2, 2013

### modulus

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

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?

7. Mar 2, 2013

### marcusl

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.

8. Mar 2, 2013

### ZapperZ

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

Zz.

9. Mar 2, 2013

### Staff: Mentor

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. Mar 3, 2013

### modulus

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...