Long Range Repulsion,
Short Range Attraction
Part of a Series of Activities in Plasma/Fusion Physics
to Accompany the chart
Fusion: Physics of a Fundamental Energy Source
Teacher's Notes
Robert Reiland, Shady Side Academy, Pittsburgh, PA
Chair,Plasma Activities Development Committee of the
Contemporary Physics Education Project (CPEP)
Editorial assistance: G. Samuel Lightner, Westminster College, New Wilmington, PA and Vice-President of Plasma/Fusion Division of CPEP
Advice and assistance: T. P. Zaleskiewicz, University of Pittsburgh at Greensburg, Greensburg, PA and President of CPEP
Prepared with support from the Department of Energy, Office of Fusion Energy Sciences, Contract #DE-AC02-76CH03073.
©2002 Contemporary Physics Education Project (CPEP
Preface
This activity is intended for use in high school and introductory college courses to supplement the topics on the Teaching Chart, Fusion: Physics of a Fundamental Energy Source, produced by the Contemporary Physics Education Project (CPEP). CPEP is a non-profit organization of teachers, educators, and physicists which develops materials related to the current understanding of the nature of matter and energy, incorporating the major findings of the past three decades. CPEP also sponsors many workshops for teachers. See the homepage for more information on CPEP, its projects and the teaching materials available.
The activity packet consists of the student activity and these notes for the teacher. The Teacher’s Notes include background information, equipment information, expected results, and answers to the questions that are asked in the student activity. The student activity is self-contained so that it can be copied and distributed to students. Teachers may reproduce parts of the activity for their classroom use as long as they include the title and copyright statement. Page and figure numbers in the Teacher’s Notes are labeled with a T prefix, while there are no prefixes in the student activity.
Developed in conjunction with the Princeton Plasma Physics Laboratory and funded through the Office of Fusion Energy Sciences, U.S. Department of Energy, this activity has been field tested at workshops with high school and college teachers.
We would like feedback on this activity. Please send any comments to:
Robert Reiland
Shady Side Academy
423 Fox Chapel Road
Pittsburgh, PA 15238
e-mail:
voice: 412-968-3049
Long Range Repulsion, Short Range Attraction – Page T1
Long Range Repulsion, Short Range Attraction
Teacher’s Notes
Part of a Series of Activities in Plasma/Fusion Physics
to Accompany the chart
Fusion: Physics of a Fundamental Energy Source
Introduction:
One of the harder ideas to grasp in fusion is that nuclei, which strongly repel at long range (compared to the size of a nucleus), can strongly attract at short range. This activity produces a magnetic example of repulsion switching to attraction as two objects get closer together. It does not work the same way as the forces between nuclei work; electrical repulsive force overwhelmed by short range (residual strong) attractive nuclear force. However, it does provide an analogous example of forces (magnetic in this case) switching in direction as the separation distance in reduced.
This activity can be used directly in a unit on nuclear physics or fusion and plasma physics. However, it is just as likely to fit in a unit on magnetism in which it will help students to use a magnetic pole model of magnetic forces to explain magnetic forces between permanent magnets and ferromagnetic materials such as iron or steel. Then its application to understanding fusion can be brought in as an extra topic.
Materials:
pair of neodymium or cobalt-samarium disc magnets*
steel rod*
machine nuts*
steel ball bearing*
Optional: iron filings
* Comment on Dimensions:
What works best is for the ball bearings and machine nuts to have similar diameters to the disc magnets, but the effect works for a range of diameters of at least a factor of two.
Please see the discussion in the next section for more detail.
Background:
The basic ideas behind the model are that like poles, such as two north poles, will repel one another, unlike poles attract, and a pole of a permanent magnet will induce two poles in a nearby piece of unmagnetized steel. Specifically, a north pole brought near a piece of steel will induce the development of a south pole on the side of the steel closest to the magnet and a north pole farther away. If the piece of steel is small, it will simply become “polarized” and act as an extension of the magnet (see Figure T1).
Figure T1: As the unmagnetized piece of steel shown in (a) is moved toward the permanent magnet on its left, magnetic north and south poles begin to be induced in it (b). These will cause it to act like an extension of the permanent magnet once the piece of steel reaches the permanent magnet (c).
If it is long, as is a steel rod, the end nearest the magnet will develop one pole, but the other end will be too far away to be affected. Instead, the second pole will be inside the rod and relatively close to the permanent magnet that induces the poles (see Figure T2).
Figure T2: Induced south pole on the near end of a long steel rod is close to the inducing north pole of the permanent magnet while he induced north pole is just a short distance inside the rod. The far end of the rod is not magnetized by the permanent magnet.
Since the induced pole closest to the magnet affecting the piece of steel is opposite in type to the pole inducing it, this induced pole will be attracted by the permanent magnet. At the same time (as expected from Newton’s Third Law) this closest induced pole will attract the permanent magnet. The repulsive forces between the original pole and the induced like pole acts at a greater distance than does the above mentioned attractive force and so is weaker. Thus the net force between a permanent magnet and a previously unmagnetized piece of steel is always attractive (see Figure T3).
Figure T3: The net force on the steel object on the right (by Newton’s Third Law opposite to the net force on the permanent magnet) shown in (b) is the vector sum of the forces exerted by the permanent poles (1 and 2) of the magnet on the induced poles (3 and 4) shown in (a). This vector sum is shown to be attractive in (b). This illustration shows a typical situation in which the net force is dominated by the closest poles and when they are opposite as shown, that will be attractive.
The odd effects that will be seen with a ball bearing and with two machine nuts between the like poles of two permanent magnets can be explained by the production of two poles by each of the two permanent magnets. This is a quadrupole with two like poles in the center of the ball bearing (see Figure T4 following answer to procedure question 4) or two like poles pushing the machine nuts apart (see Figure T5 following answer to procedure question 5). With a typical pair of neodymium or cobalt-samarium disc magnets the steel rod should be at least ten centimeters (four inches) long, the two steel machine nuts at least half a centimeter (one quarter inch) thick and the steel ball bearing of about one centimeter (nearly one half inch) diameter. However, all this can vary, and you should try different sizes of ball bearings and machine nuts to find what works best with your magnets before presenting this to students.
With a little guidance, most students will be able to figure out how the model explains what they see. But expect a period of surprise before they get into problem solving.
Answers to questions in procedures:
1.Holding on very tightly to the two disc magnets, one in each hand, bring the flat sides of the two magnets toward each other. You should feel the effects of either an attractive or a repulsive force. Reverse one of the magnets to reverse the effect. In the case of the repulsive effect, slowly bring the magnets toward each other until they touch. You will have to hold them very firmly to do this. Does the effect ever become attractive?
Answer: No.
2.While firmly holding the two magnets, locate two sides that repel as in the previous procedure. Hold the two magnets far apart, but keep the repelling sides (called like magnetic poles) toward each other. Maintaining this alignment, place the steel rod between the two magnets so that each end of the bar is near a magnet (see Figure 1). Slowly bring the magnets closer to the ends of the rod until one, then the other, touches the rod. Does the effect ever become repulsive?
Answer: No. The two magnets are too far away from each other to repel. Each polarizes its end of the bar and is attracted to the induced pole nearest to it.
- Again locate two repelling poles of the magnets. Separate these poles, but keep them toward each other. Maintaining this alignment, place the ball bearing against one of the repelling poles while the other magnet is several centimeters away from the ball bearing (see Figure 2). Slowly and carefully bring the second magnet toward the ball bearing until contact is made. Do this several times to be sure of what is happening. How is the result like that of the repulsive part of Procedure 1? How is it like that of Procedure 2? Can the results be explained in terms of what happened in the previous procedures?
Answers: It is like the result of Procedure 1 in that repulsive forces are felt initially when the second magnet is relatively far from the ball bearing. It is like the result of Procedure 2 in that both magnets end up being attracted to the ball bearing like they were attracted to the steel rod. The initial repulsion indicates that the side of the ball bearing away from the magnet that it is initially touching and held to is like an extension of that magnet. Just as that magnet would have repelled the other, as the two are oriented, the ball bearing repels the second magnet. The final attraction indicates that the second magnet has been able to polarize its side of the ball bearing, and each magnet is symmetrically producing polarization of the ball bearing in the same way that each magnet had polarized the steel rod (see Figure T4).
Figure T4: “Pole” representations of how forces go from repulsive at long range (a) to attractive at short range (b) and (c). For simplicity, only the north poles of the magnets are illustrated in (b) and (c).
4.Again locate two repelling poles. Separate these poles, but keep them toward each other. Maintaining this alignment, place both machine nuts flat against one of the repelling poles while the other magnet is several centimeters away from the machine nuts (see Figure 3). Slowly and carefully bring the second magnet directly toward the machine nuts until contact is made. Were there any surprising results?
Answer: Yes. One of the machine nuts suddenly jumps away from the other and onto the second magnet (see Figure T5).
Figure T5: “Pole” representation of how the machine nuts come to repel one another as the second magnet (right one) changes the polarization of the machine nut nearest to it. For simplicity only the north poles of the permanent magnets are illustrated.
If not, try again, and move more slowly. Would the same forces which acted within the ball bearing in the previous procedure cause the machine nuts to separate in this one?
Answer: Yes, with one exception. In the center of the ball bearing will be two like poles that repel each other just as the like poles induced on the contact sides of the machine nuts repelled each other. The difference is that within the ball bearing there are attractive forces from atomic bonding that keep it together.
Answers to Questions:
- How many magnetic poles are induced in a ball bearing in contact with a single magnet?
Answer: Two. In classical electrodynamics there is no way to produce a single pole, i.e., what is called a monopole. Even though the production of monopoles is not forbidden within quantum electrodynamics, no monopole has ever been observed. Consequently, it currently seems that magnetic poles must be produced in pairs, as illustrated in Figures T1 through T5. If the magnet had a north pole against the ball bearing, it would induce a south pole on the near side of the ball bearing and a north pole on the far side. It would in effect polarize the ball bearing so that the bearing would seem like an extension of the magnet.
2.How many poles were induced in the steel rod when both magnets were in contact with its ends? Where along the rod might these poles be located?
Answer: Four poles. Each magnet would polarize the side of the rod it was closest to. If north poles of the magnets were both against the rod, each would induce a south pole next to itself and a north pole a little further away in the rod.
3.What evidence do you have that the same number of poles were at times induced in the ball bearings and in the pair of machine nuts as in the steel rod? Where would these poles be in the ball bearings and in the pair of machine nuts?
Answer: Two things happened to support this. The first is that both magnets ended up being attracted to the ball bearing and to the machine nut closest to it -- just as they were both attracted to the steel rod (see Figures T2, T4, and T5). The second is that the machine nuts repelled each other when the second magnet got close to them. This indicates that there were two like poles on the parts of the machine nuts furthest from the magnets and closest to each other. To see that there are poles induced in the steel rod when the magnets are at both ends of the rod, put a piece of paper over the rod and magnets, and sprinkle some iron filings over the paper. You will see filings concentrating around the magnets and at two locations away from the magnets toward the center of the rod.
- Would you view the ball bearing with both magnets against it as a tripole or as a quadrupole? Why?
Answer: A quadrupole (see Figure T4(c)). As indicated in the answer to Question 1, magnetic poles are always formed in pairs. The center of the ball bearing acts like a single pole opposite to in type but of twice the strength as each of the poles that form next to the magnets. The fact that it is of twice the strength as the other poles is consistent with thinking of it as two poles very close together.
- For nuclear fusion to take place, the long range electrical repulsion between nuclei must be overcome by a short range nuclear force attraction. If this didn’t happen:
a.could stars come into existence gravitationally?
b.could stars radiate large amounts of energy fairly continuously for billions of years?
c.could massive elements form in stars?
Answers:
- Yes. The gravitational force responsible for the condensation of interstellar gases and dust into stars is always attractive and not dependent upon nuclear or electrical forces.
b.No. Stars could convert gravitational potential energy into radiant energy for millions of years while shrinking in size, but the rate would decrease over time and become relatively insignificant after a billion years.
c.No. Stars produce elements up to iron through nuclear fusion. If there were no short range force to allow lower mass nuclei to stay together to form higher mass nuclei, hydrogen would be the only element in the universe. No nucleus with more than one proton would be stable. In supernovae, elements with atomic number beyond that of iron are formed in energy absorbing (endothermic) nuclear reactions.
6.What would the night sky look like if objects that repel at some separations did so at all separations?
Answer: Very, very dark. Actually there would be no Earth as such and no day or night. Earth is made mostly of elements that would not form in a universe in which nuclear fusion couldn’t occur.
APPENDIX
Alignment of the Activity
Long Range Repulsion, Short Range Attraction
with
National Science Standards
An abridged set of the national standards is shown below. An “x” represents some level of alignment between the activity and the specific standard.
National Science Standards (abridged)Grades 9-12
A. Science as Inquiry
Abilities necessary to do scientific inquiry / X
Understandings about scientific inquiry / X
B. Physical Science Content Standards
Structures of atoms / X
Motions and forces / X
Conservation of energy / X
Interactions of energy and matter / X
D. Earth and Space
Origin and Evolution of the Universe / X
E. Science and Technology
Understandings about science and technology
G. History and Nature of Science
Nature of scientific knowledge / X
Alignment of the Activity