Compilation: Fields Conceptual Issues

Compilation: Fields -- conceptual issues

Compilation: Fields -- conceptual issues

Date: Sat, 3 May 2003

From: Ron McDermott <>

Out of curiosity, I'd be interested in the conceptions we use for presenting the idea of "field" to our kids. There are a number of issues that are problematic in my opinion, and I'm wondering if anyone has a vision of this that eludes me. This does not matter, perhaps, for the average kid, but for the potential physicist or engineer, it seems to me that it would. I'd be interested in comments, particularly from Gregg.

There are at least three conceptual issues, imo:

1. We speak of the field "generated" by an object, such that a second object "in the field" of the first experiences a force. Yet in Modeling we emphasize that a force is shared between, or subject to the action of TWO objects. These two ideas seem inconsistent to me. How do/should we resolve this inconsistency for our students?

2. If the first object has a field, so does the second object. The traditional concept (above) tends to focus the kids on there being ONE field for the first object, and to ignore the field of the second object. This seems to be a breeding ground for problems.

3. The field can transfer energy TO an object (or an object to the field) through work. Thus the field acts as if IT were an object. How do we account for this?

This stuff never bothered me prior to my exposure to Modeling <g>! If it wasn't for the field transferring energy, one could avoid the complications by saying that the concept of "field" is a construct and need not be thought of as being "real" in the usual sense. That option, however, does not seem to be available. We can get around the first two problems, perhaps, by making the analogy that a "field" can be thought of as tentacles extending from an object into the space around it, and when the tentacles of TWO objects interact, a force is generated (which can be either attractive or repulsive depending on the nature of the field). This would seem to require three different sets of tentacles that are keyed to electric, magnetic, and gravity, but we could tie this up by postulating that the tentacles have different kinds of "hooks" embedded that could link up with other tentacles in different ways and generate different kinds of forces (electric, magnetic, gravitational). What do you think about "tentacles" as an analogy?

The "tentacles" can act as springs that can stretch or compress, so energy transfers could be accounted for, and we COULD use the "tentacles" as the second "object", but "object" seem to require an entity with size, mass, etc. Since "field" doesn't seem to fit, how do we deal with that problem? Maybe we can't? I'd be interested in other ideas/analogies; what do you think?

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Date: Sat, 3 May 2003

From: Gregg Swackhamer

Ron McDermott wrote:

THERE IS AN ISSUE HERE. BUT WITHOUT A FIELD YOU HAVE ANOTHER ISSUE: ACTION-AT-A-DISTANCE. HOW DOES OUR BODY OR THE MOON KNOW THAT THE EARTH IS THERE? TO AVOID THIS PROBLEM, IT IS HELPFUL TO SAY THAT FIELDS ARE THE MEDIATORS OF SUCH FORCES. FOR ORDINARY OBJECTS ON THE MACROSCOPIC SCALE WE CAN RELY ON CONTACT FORCES. BUT MODELING HAS ALWAYS ASKED STUDENTS TO LOOK BEYOND ONLY CONTACT FOR OTHER FORCES THAT WE CALLED "LONG RANGE FORCES". I JUST SAY THESE FORCES ARE REALLY EXERTED BY FIELDS. THAT MAKES ALL FORCES LOCAL. BUT IT DOES MEAN THAT WE CANNOT SAY OBJECT A ACTS DIRECTLY ON OBJECT B AND VICE VERSA. OH WELL. PICK YOUR POISON.

THE WORD FIELD IS USED IN TWO SENSES. ONE IS THE STRENGTH AT A POINT OF

THE FIELD CREATED BY ONE KIND OF CHARGE OR ANOTHER (GRAVITATIONAL CHARGE 3D MASS, ELECTRICAL CHARGE =3D CHARGE, STRONG CHARGE =3D COLOR, MAGNETIC CHARGE =3D CURRENT ELEMENT). THE OTHER USE OF "FIELD" REFERS TO THE ENTIRE FIELD GLOBALLY INCLUDING ALL SOURCES OF INTEREST. WE MUST DISTINGUISH BETWEEN THESE USES OF THE WORD.

3. The field can transfer energy TO an object (or an object to the field) through work. Thus the field acts as if IT were an object. How do we account for this?

FIELDS ARE PHYSICAL SYSTEMS IN THEIR OWN RIGHT. THEY ARE NOT JUST FICTITIOUS CONCEPTS USED TO HELP GET ANSWERS. THEY HAVE PROPERTIES LIKE ENERGY, MOMENTUM, AND ANGULAR MOMENTUM. IT IS INTERESTING THAT THE ELIMINATION OF THE AETHER AS A CONCEPT 100 YEARS AGO MADE FIELDS SEEM TO BE FICTITIOUS FOR A WHILE. THE IDEA THAT FIELDS ARE UNREAL THINGS STILL LURKS IN OUR BOOKS EVEN AFTER ABOUT 100 YEARS OF THE UNDERSTANDING THAT FIELDS DO NOT NEED THE AETHER TO EXIST.

A MECHANISTIC VIEW OF FIELDS HAS A GOOD PEDIGREE. FARADAY AND MAXWELL TRIED TO DO IT. BUT THEIR IDEAS DON'T WORK ULTIMATELY. ONLY THE QUANTUM FIELD THEORY GUYS (LIKE IN FEYNMAN'S LITTLE BOOK QED) HAVE A MECHANISM, THE EXCHANGE OF VIRTUAL QUANTA. I HAVE NO PRESCRIPTION FOR INTRODUCING FIELDS YET. IT IS A REAL ISSUE, AND IF FIELDS CAUSE A TEACHER MORE PROBLEMS THAN THEY CURE, I WOULDN'T WORRY ABOUT INTRODUCING THEM. BUT I USE A STUDENT'S SUGGESTION: THINK OF THEM AS HALOS AROUND CHARGED OBJECTS THAT EXERT FORCES AND STORE ENERGY. THAT'S ALL THE REALITY THAT I NEED FOR A FIELD. IT IS A SORT OF DESCRIPTIVE MODEL. I TAILOR THE MODEL TO THE COMPLEXITY THAT WE NEED, WHICH AIN'T MUCH.

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Date: Sun, 4 May 2003

From: Ron McDermott <>

Granted, this is the current explanation, but I can't see a way to make this explanation useable for students to "hang their hat on". The concept of "field" is at least intuitive and visual, it is just that it suffers from the conceptual problems I listed. Heck, I can't make sense of this "exchanging particles" stuff; how can I expect my kids to? ;-)

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Date: Mon, 5 May 2003

From: Matt Greenwolfe <>

Here's how I try to deal with these issues, but I find it confusing as well, the more so since I've started modeling, because the graphical representations show what is happening so clearly. This means the conceptual difficulties are more evident, and my students are asking more detailed conceptual questions that I'm having trouble answering. I would appreciate comments/feedback.

In response to question 2, I tell the students that, indeed, all objects create fields and all of them feel forces from that field. However, an object does not feel a force from its own field. This means if we are interested in calculating the force on a particular object, then we are interested in the fields created by everything *but* that object. The particular object in question still creates a field, but that field is irrelevant to the calculation of force on that object. After a while and some serious thought, this does help my students figure out which objects in a problem should be viewed as the source of a field and which should be viewed as feeling a force (and possibly also receiving a transfer of energy) from the field. I repeat the words "source and force" often to help them focus on this.

Now I know that objects do, in fact, feel forces from their own fields, and this gives rise to induction as well as infinite terms in quantum field theory that Feynman figured out how to get around, etc. But that is all way more than I want to approach with my high school students.

In response to question 3, I do have students draw a bubble for the field itself in their system schemas and think of it as something real, although not an object in the sense of matter, that can store energy, exert forces, and transfer energy. After all, if it's not real, and it can't do these things, then how does it help to explain the paradox of action at a distance? I also have them draw force maps for the field, showing equal and opposite pairs of forces of the field on an object, and of the object on the field.

I start this with an experiment I picked up earlier from this list serve. I place a coil of magnet wire wound around a plastic film canister onto a balance. Above that coil, I suspend another magnet from the bottom of a second balance. (My balances have hooks on the bottom for this.) When current flows through the coil, equal and opposite forces are recorded by the balances. I then have them draw a system schema for the coil, the magnet, *and* the field. And draw force maps for the coil, the magnet, and the field. Later on, (with gravitational and electric fields) I have them add arrows to their system schema to represent energy transfer to or from the field. So in answer to Ron's first question, the field is included as one of the "objects" involved in the force. This does clarify the role of the field for the students, but in doing so, does this treat the field too much as if IT were an object?

This year, I also avoided defining the word "field" for the students, and instead after postulating its existence and drawing the diagrams after the experiment above, I asked them for their definition. I did this a couple times per week throughout the field unit, and gradually, they were able to articulate the main ideas in their own words. I think this worked better in terms of getting them to understand what a field was and why it was invented.

Ron also writes:

>Heck, I can't make sense of this "exchanging particles" stuff; how can I expect my kids to? ;-)

I've had some trouble with this one, too, since grad school. I can understand how exchange of particles could lead to a repulsive force as one particle recoils after emitting the intermediary particle, and another is "pushed" when it receives the particle. But how can exchange of particles create an attractive force? If someone could help me here, I would greatly appreciate it!

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Date: Mon, 5 May 2003

From: Chris Horton <>

My reading in student preconceptions in chemistry led to a study which found that the tentacle model of forces between atoms underlay one of the central preconceptions of molecular bonding: the view that an atom has a particular amount of force available to bind to other atoms and that when enough of the force is in use the atom is neutralized. Translate: when all of the tentacles are attached there are no more available. So use this model with great caution, or avoid it altogether.

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Date: Mon, 5 May 2003

From: Jean OOSTENS <>

You can explain fields deriving from a potential as soon as you cover partial derivatives. This is first year college material in Europe. Simple cases (in one dimension) can be explained with elementary calculus, using only derivatives. One needs to make the subtle distinction between the Potential function and the potential energy: the potential is only defined within an arbitrary constant, while the potential energy has a chosen natural zero (Sea level for mgh, relaxed position for a spring...)

Energy resides in fields: Take a capacitor with a dielectric constant epsilon-r, plate area A and separation d. Energy = C V^2 / 2 becomes, in terms of the field E = V/d Energy = epsilon-o epsilon-r A ( d E )^2 / 2 d = epsilon-o epsilon-r A d E^2 /2 as A d is the volume between the plates, where the field is uniform, the energy per unit of volume becomes

Energy/Volume = epsilon-o epsilon-r E^2 / 2. This shows that the energy stored in the capacitor is localized in the field.

A similar derivation can be done for the magnetic field: the energy producing the spark in a car engine is first stored in the iron of the ignition coil. The magnetic field disappears suddenly when the primary current is interrupted. The energy is transferred to the spark inside the combustion chamber.