Compilation: Fields -- conceptual issues
Compilation: Fields -- conceptual issues
Date: Sat, 3 May 2003
From: Ron McDermott <rmcder@PEOPLEPC.COM>
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?
---------------------------------------------Date: Sat, 3 May 2003
From: Gregg Swackhamer
Ron McDermott wrote:
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?
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
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Compilation: Fields -- conceptual issues
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.
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.
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.
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?
A MECHANISTIC VIEW OF FIELDS HAS A GOOD PEDIGREE. FARADAY AND
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Compilation: Fields -- conceptual issues
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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Compilation: Fields -- conceptual issues
-----------------------------Date: Sun, 4 May 2003
From: Ron McDermott <rmcder@PEOPLEPC.COM>
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? ;-)
---------------------------Date: Mon, 5 May 2003
From: Matt Greenwolfe <matt_greenwolfe@CARYACADEMY.ORG>
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.
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Compilation: Fields -- conceptual issues
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!
---------------------------------Date: Mon, 5 May 2003
From: Chris Horton <chrisahorton@YAHOO.COM>
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.
---------------------------------Date: Mon, 5 May 2003
From: Jean OOSTENS <joostens@CAMPBELLSVILLE.EDU>
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.
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