TEACHING ELECTRODYNAMICS TO THE HARD-NOSED

D CDan Censor, Ben Gurion University of the Negev, Department of Electrical and Computer Engineering,Department of Electrical and Computer Engineering,Beer Sheva, Israel 84105, censor@ee.bgu.ac.il,

Download present presentation from http://www.ee.bgu.ac.il/~censor/presentations-directory/http://www.ee.bgu.ac.il/ censor/presentations directory/Choose files: History-marked.pdf teaching-electrodynamics-skopje-2010.ppt

hi l d i k j 2010 dfteaching-electrodynamics-skopje-2010-ppt.pdf

1

Based on: INTEGRATIVE ENGINEERING ELECTRODYNAMICSINTEGRATIVE ENGINEERING ELECTRODYNAMICS http://www.ee.bgu.ac.il/~censor/integrative.pdf (password: course) APPLICATION-ORIENTED RELATIVISTIC ELECTRODYNAMICS (2)ELECTRODYNAMICS (2)http://www.ee.bgu.ac.il/~censor/relativity-directory/relativ2-paper.pdf

d ki h i l t h lf t f t hiand many many working hours in almost half a century of teaching…

2

F C B th ld R S Th f t

3

Fresco, Casa Bartholdy, Rome. Scene: The seven fat years

Arthur Reginald. Title:Joseph Interpreting Pharaoh's Dream, 1894

4

Arthur Reginald. Title:Joseph Interpreting Pharaoh s Dream, 1894

5

After seven bad years, sad cows…

…will laugh again!

6

S t i Oh id

7

Sunset in Ohrid

ABSTRACT—This presentation brings together the personal experience (acquired over a span of almost half a century, in various countries and institutions) of teaching one-semester courses in Electromagnetic Field Theory and in Advancedcourses in Electromagnetic Field Theory and in Advanced Electrodynamics, to students, both under and post graduate, whose priority is not theoretical subjects, like engineers and applied physicists The ultimate challenge is to engage them by devisingphysicists. The ultimate challenge is to engage them by devising curricular packages that are succinct and self contained but still of high level. We wish to equip our students with precise concepts, while keeping the mathematics at a level that they are skilled to handle. Moreover, we wish to instill in them the intuitive thinking needed to tackle problems related to their future specializations.p p

8

*Why is the theory so important for application- oriented Students?

*How can we convince them they need it?

*What teaching methods should we use to achieve skills, without getting bogged down by the

detailed proofs of mathematical theorems?detailed proofs of mathematical theorems? Laplace equation for potential field 2 0 r , r

applies to temperature in simple source free domains.

22 0T r

9

THE EXTREMAL VALUE THEOREM A closed surface S encloses a volume V. Given a potential field 2 0 r , with the minimal and maximal equipotential surfaces indicated. If V is q pchargeless, then the extremal potential values within V occur on S too.

max

T Vmin

TU

V

S

The proof is by reductio ad absurdum). Suppose there exists within V a closed equipotential surface T , which does not cut or touch S, whose potential is higher than the maximum occurring on S

10

whose potential is higher than max , the maximum occurring on S.

max

minT

UV

S

There is a potential gradient, and in close proximity to T there will exist another closed equipotential surface U, whose potential is incrementally lower than that on T. Hence there exists a field D, everywhere pointing outwards from T to U, in the direction of the outward normal. Integrate

QdVd SD on the closed surface T All D field vectors pointQdVdVS

SD on the closed surface T. All D field vectors point

outwards therefore the integrand has always the same sign--the integral is nonvanishing Therefore there must exist a charge Q within T But thisis nonvanishing. Therefore there must exist a charge Q within T. But this violates the initial assumption that there are no charges within V, hence equipotential surfaces within V not cutting or touching S, cannot exist, and the theorem is proven The same technique is used to show that thereand the theorem is proven. The same technique is used to show that there cannot exist surfaces within S that do not touch S, whose potential is lower than min .

11

12

13

14

15

16

17

Should we start by presenting electromagnetic theory in a historical-phenomenological manner with all the y p gseparate “laws”, like many textbooks do, and spend time on consolidating previously studied mathematical tools: vector

d t l i th f diff ti l ti ? Oand tensor analysis, theory of differential equations? Or should we jump into the pool at the deep end, starting with the Maxwell equations and clarifying specific points asthe Maxwell equations and clarifying specific points as they are encountered?

History

18

STARTING WITH ME CLARIFIES THE PREMISESSTARTING WITH ME CLARIFIES THE PREMISESWe start with the postulated Maxwell Equations (ME), ‘law’? Anyhow, what is the meaning of ( ), w ? y ow, w s e e g o“low of nature”?

,t t r rE B H D j, 0 r rD B

19

Coulomb's force (CF) ‘law’ qF E , associates mechanicalCoulomb s force (CF) law qF E , associates mechanicalF and E , is a definition! We can only measure directly F . Lorentz force (LF) (‘formula’? ‘law’?) ( )q F E v B sets CF as a limiting case for 0v . Special Relativity (SR) shows CF and LF the two are identical. LF cannot be derived from MELF cannot be derived from ME.ME+LF+SR is a complete model of electromagnetism. ME are indeterminate (#variables > #equations), therefore( q )we need additional constitutive (material) relations (CR).

20

THE INTEGRATIVE APPROACHTHE INTEGRATIVE APPROACH

,S V

d dV Q r D D S Electrostatic Gauss ‘law’

0, 0S

d r B B S Magnetic Gauss ‘law’

0, 0d E E L Electric Kirchhoff voltage ‘law’0, 0L

d r E E L Electric Kirchhoff voltage law

. . .,t t t t e m fL S S

d d d d d U r E B E L B S B S L S S

Magnetic Faraday ‘law’ 0, 0

L

d r H H L Magnetic Kirchhoff voltage ‘law’ L

,tL S

d d r H D j J H L J S Ampere’s ‘law’

,t t t tL S S

d d d d d r H D H L D S D S Electric Faraday ‘law’

21

(tongue in cheek)

, 0, 0tS

d r rH D j J J J S Kirchhoff current ‘law’

0 I d d dV d Q j j S Continuity also0,t t tVS

I d d dV d Q r j j S Continuity, also

charge conservation ‘law’. Current definition tI d Q ?? tI d Q ?? Tongue in cheek…

j v is a constitutive eqation! ˆ ˆ, j v j v z z / /I jd d d d d d dQ d/ /I jdxdy dxdydz dt dQ dt

22

CONSTITUTIVE EQUATIONS D E , B H , , ,

, , ( )s c si i i rD E H j j D j E j v , “current is moving charges”j v , current is moving chargesj E , Ohm’s ‘law’ j E

j Ej v

the two relations are incompatible

All above constitutive parameters are constants

23

DISPERSIVE CONSTITUTIVE OPERATORSDISPERSIVE CONSTITUTIVE OPERATORS1 1

2 2( ) ( ) ( )i t i ttf t f i e d f e d

2 2

12

( ) ( ) ( )

( ) ( ) ( )

t

i tt t t

f f f

f e d f

2( ) ( ) ( )t t tf e d f

( ) ( ) ( ) ( ) ( ) ( )i D E D E

( ) ( ) ( )t

t t d

D E

1 12 2( ) ( ) ( ) ( )i t i tt e d i e d

D D E

12( ) ( ) ( ) ( ) ( )i t

t tt e d t

D E E

24

MOVING REFLECTOR DOPPLER EFFECTMOVING REFLECTOR, DOPPLER EFFECTWorks only for this special case: no Loretz transformation but is relativistically exact!y

c v c y

11,

k

iE

vk

rE

rH2

ik

iHrk

x

z

Total Lorentz force TF acting on moving non-accelerated electron charge q vanishes: 0F

25

non accelerated electron charge q vanishes: 0T F

y

ik

iE

iH

vrk

rE

rH2

x

11,

i

z,

( ) 0T i r T i r

T T T i rq

E E E H H HF E v H F F

T T T i r

( )i i r r E v H E v H

ˆ ˆ ˆ ˆ ˆ ˆ( ( ) )ˆ ˆ ˆ ˆ

i i r i

i i r i

E v H E v HE vH E vH

y x z y x zy y y y

/ / / , 1 /

(1 / ) (1 / )i i r r phE H E H c v

E v c E v c

(1 / ) (1 / ),/ / (1 / ) / (1 / )

i r

r i r i

E v c E v cE E H H v c v c

26

ik

iE

vrk

rE

rH2

y11,

iH x

z

The phases of the incident and reflected waves must be equal at all times at the boundary i emust be equal at all times at the boundary, i.e., at vtx k x t k x t x vt ,

, /i i r r

i i r r

k x t k x t x vtk vt t k vt t k c

/ / (1 / ) / (1 / )r i r ik k v c v c

which is the exact result given by Einstein 190527

g y

TRADITIONAL AND TOPSY-TURVY SR Before you ask: Topsy-Turvy means upside downBefore you ask: Topsy Turvy means upside down…

28

29

These are my favorite two pigs “Topsy” and “Turvy”30

These are my favorite two pigs, Topsy and Turvy

This is not Topsy-Turvy, this is Pushmi-Pullyu

'Lord save us!' cried the duck 'How does it make up its mind?'

31

Lord save us! cried the duck. How does it make up its mind?

DOCTOR DOLITTLEDOCTOR DOLITTLETOLD BY HUGH LOFTING

ILLUSTRATED BY THE AUTHOR32

ILLUSTRATED BY THE AUTHOR

c c Lorentz Trx.

Lorentz Trx. Maxwell Eqs. (Maxwell Eqs.)’ Field Trxs.

c cLorentz Trx.

Lorentz Trx. Maxwell Eqs. (Maxwell Eqs.)’Field Trxs.

33

c c

A Einstein “Zur Elektrodynamik bewegter Körper”A. Einstein, Zur Elektrodynamik bewegter Körper ,

Ann. Phys. (Lpz.), 17, 891-921, 1905;

E li h t l ti “O th l t d i f i b di ”English translation: “On the electrodynamics of moving bodies”,

The Principle of Relativity, Dover.

34

c c

2( ), ( / )ˆ ˆ ˆ( 1) / | |

t t t c r U r v v rU I

2 1/2

ˆ ˆ ˆ( 1) , / , | |(1 ) , /

v vv c

U I vv v v v

Oversimplified!! u c

2( ), ( / )x x vt t t vx c

p

2

2

( ), ( )/ ( ) / ( / )

( ) / ( / ) ( ) / ( / )u dx dt dx vdt dt vdx c

2( ) / (1 / ) ( ) / ( / )( ) / ( / )

u v vu c c u v c vu cu c u c c v c vc c c

35

t m t m

r rE B j E B jH D j H D jt e t e

r r

r r

H D j H D jD De e

m m

r r

r rB B( , )... ( , )...t t E E r E E r

36

2( / ) ( )c U v v'( / ), ( )t t tc r r rU v v

2

2

' ( ), ' ( / )

' ( / ) ' ( )

c

c

E V E v B B V B v E

D V D v H H V H v D

( / ), ( )

ˆ ˆ(1 )

c

D V D v H H V H v D

V I vv 2

, , , , , ,' ( ), ( / )e m e m e m e m e m e m c j U j v v j

37

c c Lorentz Trx.

Lorentz Trx. Maxwell Eqs. (Maxwell Eqs.)’ Field Trxs.

c cLorentz Trx.

Lorentz Trx. Maxwell Eqs. (Maxwell Eqs.)’Field Trxs.

38

2( ), ( / )t t t c r U r v v r

ˆ ˆ ˆ( 1) , / , | |v v U I vv v v v 2 1/2(1 ) , /v c

b i h G lil iFor c we obtain the Galilei trx.1t t t r r v U I , , , 1t t t r r v U I

The Galilei trx. is not the limit of the Lorentz trx. For small v

39

FOURIER TRANSFORM MINKOWSKI SPACEFOURIER TRANSFORM, MINKOWSKI SPACE,AND DOPPLER EFFECT

Idiot! take the inverse Fourier transform, Meow…

40

FOURIER TRANSFORM MINKOWSKI SPACEFOURIER TRANSFORM, MINKOWSKI SPACE,AND DOPPLER EFFECT

M C E h “R l i i ” 195341

M. C. Escher, “Relativity”, 1953

FOURIER TRANSFORM MINKOWSKI SPACEFOURIER TRANSFORM, MINKOWSKI SPACE,AND DOPPLER EFFECT

42

( ) ( ) ii if x y z ict q f k k k e dk dk dk d 4

( , , , ) ( , , , )

, , (2 )x y z x y zc c

ix y z c

f x y z ict q f k k k e dk dk dk d

k x k y k z t t ict q

( , ), ( , )icict

k x k y k z t

R r K kK R K R

4 4( ) ( ) ( ) ( ) ( ) ( )

x y z

i i

k x k y k z t

f q d f e f d f e

K R K R

K R K R

R K K K R R

2

( ) ( ) ( ) , ( ) ( ) ( )

( / )

f q d f e f d f e

c

R K K K R R

k U k v ( ) v k( / ), c k U k v ( ) v k

43

44

CONCLUDING REMARKS Start with Maxwell equations

Use the integrative approach g pp

45

Cl ifClarify your conceptsUse minimal mathematics

46

Don’t be a pussycat Shoot down misconceptions

47

S i i i iTeach Special Relativity using the topsy-Turvy formalismp y y

48

But not Topsy-Turvy like George BushGeorge Bush

49

C bi i dCombine science and art

50

C bi i dCombine science and art

51

Have I forgotten something??(former Israeli defence minister Amir Pretz)( )

52

THIS IS ALL, FOLKS, THANK YOU

53