Transcript Matter & Interactions

Matter & Interactions
Vol II: Electric & Magnetic Interactions
Ruth Chabay
&
Bruce Sherwood
This project was supported in part by the National
Science Foundation (Grants MDR-8953367, USE9156105, DUE-9954843, and DUE 9972420).
Opinions expressed are those of the authors, and not necessarily those
of the Foundation.
Note
This presentation is normally accompanied by
oral clarifications. However, it may be useful as
it stands to give an overview of the nature of
Volume II of Matter & Interactions.
Homework problems displayed in this
presentation are copyright John Wiley & Sons.
E&M
What’s new for students?
• Concept of electric and magnetic fields
• More sophisticated model of matter
Field
• More abstract than force
• Allows us to explain and predict
phenomena which otherwise would be
inaccessible
Model of Matter
• Previously: neutral masses (atoms)
connected by springs (bonds)
• Now: consider individual charged
particles inside matter (electrons,
nuclei)
What’s not new?
• Small number of powerful fundamental
principles (unification)
• Modeling complex physical systems
(idealization, approximations)
• Integrated activities (desktop
experiments, computer labs)
Traditional sequence:
three unrelated topics
1. Charge, force, field, flux, Gauss’s law
(2 weeks!)
2. Current, potential, circuits
3. Magnetic field, magnetic force,
magnetic induction
Deficiencies of traditional
sequence
• Three unrelated topics - no unification
• Many new abstract concepts introduced
too fast, with insufficient practice
• Magnetic field introduced late in
semester, after many other new
concepts
At end of semester, students still confused about the
difference between charge and field.
EMI sequence
• Field:
– Introduced early, used continually
– Backbone of story line, always salient
• Matter:
– Fields affect matter
– Composed of charged particles
– Mobile charges are important
Solidify field concept
•
•
•
•
•
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Introduced on first day
Central concept throughout course
B introduced very early
Retardation
Patterns of field in space important
Reference frames - relation of E & B
Unification
• DC, RC circuits analyzed in terms of
charge, field and energy (potential)
• Fundamental principles same as in
mechanics
Energy principle:  ΔVroundtrip  0
Stationary charges
Sequence of chapters
• Electric field
• Matter and electric
fields
• Electric field of
distributed charges
• Electric potential
• Magnetic field
• A microscopic view
of electric circuits
• Capacitors,
resistors, & batteries
• Magnetic force
• Gauss, Ampere
• Faraday’s law
• Electromagnetic
radiation
• Waves and particles
• (Semiconductor
devices)
Not all patterns of field are possible
Energy Conservation  No curly E
•
(stationary point charges)
 dV  0
Relate observed patterns of field to
source charge (Gauss, Ampere)
No divergent B


dB
 curly E
dt


dE
 curly B
dt
(Faraday)
(Ampere-Maxwell)
Cognitive Issues
• Primacy: E & B introduced early
– Learn concept well - continued practice
– Learn relationship of E & B through tasks
involving both
• Recency: Just-in-time flux
– Gauss’s law only after much practice
with q & E
– Gauss’s law just before Faraday’s law
Gauss’s Law
(a pedagogical case study)
• Parsimonious – very few steps in
reasoning required
• Elegant – symmetry instead of algebra
• Abstract and powerful
• Relativistically correct
Gauss’s Law in Introductory E&M
First or second week of E&M in the traditional
introductory course. Used to derive:
• E of a uniform spherical shell, plate, rod
• No excess charge in interior of a conductor
• E = 0 inside hole in a conductor
Students are rarely able to
understand or apply Gauss’s Law.
Why?
What knowledge is necessary
to understand Gauss’s Law?
• Calculus
• Physics
• Symmetry / geometry
Calculus
Students have not yet studied vector
calculus
  
E 
0
Calculus
Students have not yet studied surface
integrals

qinside

 E  nˆdA 
0
Students have not yet encountered
vectors inside integrals
Calculus
Mathematically formal, unfamiliar, and
intimidating
Physics
Gauss’s law relates patterns of electric
field in 3D space to spatial distributions
of source charges
Physics
Electric Field:
• New concept
• Abstract, still unfamiliar
• Students still vague on relation between
charge and field
Physics
Electric field
• Students have little or no experience
with possible patterns of electric field
• Have calculated E only at a single
location
• Students have no experience thinking in
3D
Symmetry
• Students have a lot of practice in algebra
(To them, this is physics reasoning)
• Students have never before encountered a
symmetry argument!
Although symmetry arguments are
powerful, they are not obvious or intuitive
without explicit instruction and practice
• Students have no experience thinking in 3D
Maximizing the chances of learning
• Introduce Gauss’s Law later, after students
have more experience with electric field
• Give students more experience with patterns
of electric field in space
• Use 2D and 3D visualization tools
• Introduce relationships qualitatively
• Connect qualitative, visual representations to
math
Gauss’s Law in Matter & Interactions
Field as primary concept throughout semester
Work with field and patterns of field for 15 weeks
Delay Gauss’s Law until week 9
Who benefits from early introduction of Gauss’s Law?
Introduce qualitatively, visually
See instructor programs at M&I web site
Limited goals
Visualization of Flux
Confusion: Gauss’s Law and Superposition Principle
(appears that E on surface is due only to q inside)
5-10 minute lecture-demonstration
(EMField)
Students spontaneously draw diagrams like those in
EMField
Final exam problem at CMU
Electron current i enters steady
state circuit
u1 > u2 and n1 > n2
Dashed line: Gaussian surface
with circular cross section and
radius < r
Determine amount and sign of
charge on the interface between
the Cu and NiCr wires.
Final exam problem: Gauss’s Law
mean = 19 / 25
12
10
8
6
4
2
0
0
2
4
6
8 10 12 14 16 18 20 22 24
Electromagnetic Radiation
• Central to course (this is the punch line)
• Radiative fields affect matter in the
usual way
• Produced by accelerated charges
• Microscopic mechanism for physical
optics (re-radiation)
Modeling in EMI
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•
•
•
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Amount of charge on a tape
Sparks in air (initial model fails)
Pick up Al foil
Polarizability of C
Magnetic moment of bar magnet
Cyclotron
Semiconductor devices
…
Computer programs written by
students, using VPython
Field of a dipole
Motion of proton in a dipole field
Field of a charged rod
Field inside & outside a solenoid
Cyclotron
Positron in a plane wave
Matter & Interactions I:
Modern Mechanics
modern mechanics; integrated thermal physics
Matter & Interactions II:
Electric & Magnetic Interactions
modern E&M; physical optics
Ruth Chabay & Bruce Sherwood
John Wiley & Sons, 2002
http://www4.ncsu.edu/~rwchabay/mi