Special Relativity and Electromagnetism, USPAS, January 2008 U N S I V P E R E U S E I Y N T Y Le I a T C

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C A 1 Special Relativity and Electromagnetism, USPAS, January 2008   Electromagnetic theory Notions ofSpecialRelativity Outline         E L M M C 4 a L H - n l o o o i v e a a d s r r n c e g x t e e

t s o c t w n n n r e i t r o m e t t o r e i z z t m c v r l i

e a l s c f t a ’

r o l

s d t a

v a g i

r b n i e o n e c n l a q d n a e c s e c u t t f

k t o a l E o i a a g t c r r i t w i n

m r i o a w o o s s n n a t n u a , ) e d

t s v n p i i

, o n e e d a n s ’ l r s e t s

i c

r c ( t e l l r e e l i a c

n c t

g s i o o c t l h n a l i l

s a c i o r o

n n p t s o r t a e c n t i t o i a n l 2 Special Relativity and Electromagnetism, USPAS, January 2008  through wavetheory explain electromagnetismandoptics Maxwell Historical background  A     

f s m I t M i L a “ o A e n r n o E l f i w a

o v

e g

a u m t e o n n c h a x h r l

r s h e e g d r w c e t d f i

c a d e

r o p a o e w e t n

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s s i m o i l

o h t c t t

’ m

b m a s equations(1863)attemptedto p o h s a i a n

t , t

m a a c f a

r i g q a a a g u o s e s a a u l

t l n n s s s l l r l t k a u t

m e s e o f h e t d r m t s n i

i a a

y o e

c o w “ e m l l n

p l m w e l

i t u s i e c t o h n

i a h m s t a c a t r t v

r a h e o s t i e e

l n r p m l e

s a i o n i e g s f c a b e o e e h t g d j t i r e s t o

n o

c h n n u e a t

a s

= v t s n w i s

s e 3 d

m i r s t × t i p

h h a 1 i

e c e n n

0 m o e r t 8 c ” d

a u m o

e t c n p n t x /

e d a o i s s r s t n e i

i t i a r s b l s n y

n t

l G

f e e

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n n w

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r h i t e t c a e h

a e a n m s

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d w s s i p c h a o e l r r t e 3 Special Relativity and Electromagnetism, USPAS, January 2008     t c 1 c L e ( M l v e F s d s S Experimental evidence i h 1 p h o o a x 9 t i e q i o 8 z a s e i r m n p 0 i e l u r c f t 8 o e r t i 4 e e t e t a r h h i

a 7 p c r

d l ) n d

r n i e

i a m i u : ) i r n t g

t t s

t l m c p o h e t

z y s

h a o t o s a s f e - r o

i e n t

t o t s F

p o o r l n d

a i n e d i a f h i o u n p g r - t

e d t b

l a n M z s

g s a h F t i h

p G e

r i h d o t ( b y r n o e c s h

e r u u a y p e t n

8 t a t b r

n l c e t

m o h t 5 l e a t i h o a

d a i n t 0 p e t y

o e d u o h f n o

)

o a r n d a l i e

t e

d o t e c t i s i x : s i ’ o h r

t i s n r s i a p t o

e e s a i

e r t

o c

n ( ﬁ h e o r t m n 1 d i i t e f n 8 o m s

a t i

9 n t h o l e 4 e l

f e n o

– f t M i c h e l s o n F i z e a u

a n d

F o u c a u l t 4 Special Relativity and Electromagnetism, USPAS, January 2008 1 1 . . Postulates e t E F a p T S f m r r n q r a h v a e i u o d u r n m e e c s p s a s r r t o

e t e t e y f

i n

r o

o P

o e t p e r

y d n x

f m c o h

s i

r y s

P I a e s

d t f t s

t s f s o

u e i i e A

o c s

s a l r r

a n

, c a

e n t i

l r l s u

B n t

i . a a e l

b c l

a n T a b a o :

e i of SpecialRelativity i w r

d n t s . b h n P e e

g o e u

i o :

t l r y s s a w u

n , i

i t t n p e o

i n n h e

c e

i v e

v c a n y i

i a v f s o n a e p s

r a e n i r a r o l i c m n t n s a e i i a b t a t d a n e s

l j a l o

e n t

l w o n e

a c f

u q r n c

t w t

n u R l

i i m y

d a n c i

n e o t n

h e

i e

i s f

l r

f a p o

h a

n i n a n

a t n t ,

s o c h

v e

i e

e t v w e

r e h n i

- t

n i

e i d c h

t i s a e

r o

m e y

l p h

- n

i t

c a n o e

i e

a o v u

e r w e o l d - e s r

d b o t i i i f

i t n c n r e r a h

a o d g a o y l

m -

t i

t s f f e a n o h

e s t n a r e l a h

d i y t

m o e e f g i

o f n

o e h

m l a r t

l h e F t t o a e f e w t ' e s , h r

t i e i e h n n m n e g e c n a r e t t i i , a

c i l a t l 5 Special Relativity and Electromagnetism, USPAS, January 2008   s m F The LorentzTransformation p u T r o o a n h v m c d e e i

n e

s - a r t p g i

f m L

a w r c o a e e i r m

t - e c h t n o e i

m v

o t z e r e

d l t

o i r i n a c n

i t n

a t

y s t r

e f

o v s

a r

a l m

r l i t o e s o a

t i a i r n g o

v f n t n r h a a s s r e m f i

o a x e r n - m

a t x w e i d s i

t t a h h s e : 6 Special Relativity and Electromagnetism, USPAS, January 2008 t a R h t o

e x d

' o Length contraction A

A b ,

s B x e '

B r o v . f

z e I

t l r s e

i n l F s e g

r c n t a h o y g m

n t L h e t '

L F f a i x

c x s t e e e e d d n

n b

y F ' v z ’ F r a y m ’ e A

F ’ R o d B x ’ 7 Special Relativity and Electromagnetism, USPAS, January 2008 are simultaneous Blue off mirror).When clocks, (lightbeambouncing Red t t c C h i o m l e o o

e r c t

i a d s k at rest,tickandtocks Time dilatation m nd

t n i A e n a

B an

d t f e lue i r s f d a f

m e

(

t x r with identical B e e , . y

I n F , n c z R

) e a m ed

t a Δ

o n a

t and v d

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i n d o s g i i

f n d

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l w a r a e m the clockof tocks butaccording to same timebetween ticksand velocity Blue t i n e t e h t d

F m ' oves withhismirrorat v .

B B lue lue

measures the

runs slow R ed , Blue = b Red m F e o

i γ t r r w

t 1 c o

t i e a h

c r = e n

i k a n n d

s n 1

. Blue R R

d , s Μ D

d ed t R i h i s s ed

a γ

t t R a a

t a

v n

B n n d R d c c

i M =

s e e m t

a b

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e r v c r 1 t t w o . w e t

r S e i e

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. B M 8 Special Relativity and Electromagnetism, USPAS, January 2008     O d R a F a T c o n t

r u e Example: RelativisticTrain b f

n i b d l r n v s a a t o

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c e l e D

e t

e m

s e D o r

n t a d s i f o , d c

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s d u t

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n i , u r n

e d e e B a

l l

o t r

a B u w d n t

n i s

i v G f e n t r h e e e a

l m t o t

o r o b a e

f t s i

r e F n 5 a r 0 ’ i

n w m e r i ! t s h    W t S p 0 r W e W g u e n ? o o r s n

e h h h t

e S p t e v n s a e a h e r e

i r t t e t e i s o c

e t n l d d ?

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g e t n

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t s

t u e

i c

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i e n e T c d l c

t k h

c h G 1 o

e r i r 0

s e , i

z e

0 t n

a w e w c a m c d r l d i i o o o

d t

w f c h

a r e i e k s n o h v n

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h n e n a a e

t n d G s d s 9 Special Relativity and Electromagnetism, USPAS, January 2008        I 4 4 4 4 4 F n 4-Vectors andEinstein - - - - - i F M A V P r v s o o a e c t o r s r

l c n m o c i i e a t e o c l i n e : e i o t t n e r t n y s a

t t : : : u t h i m o a At rest energy is i.e. whichgives Differentiating themomentuminvariant n t : :

andthusthe constantis

a n d

d ’

relation

and byintegrating Buttherateofchange kinetic .

F inally, theenergy is a nd 1 0 Special Relativity and Electromagnetism, USPAS, January 2008 i   F     n o

W H r e K M R R Velocity andKineticEnergy n e e in e h o e la la a m e e r v tiv tiv

n g tic , e y y

n r

e e e p e tu v v n l a a m e e e r t lo lo t r i i g v T c c c y i l

ity ity [ s e M t s i a

e c b V , n e

] s

d c a E m o L l m e a o c l r n e l t e

d v n r o e e tz n l l o a fa t c i i c v t to y i s

r t c i h c a

a n t g

h e i

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P c h r o a t n o g n e 1 1 Special Relativity and Electromagnetism, USPAS, January 2008 R e l a t i o n s h i p s

f o r

s m a l l

p a r a m e t e r

v a r i a t i o n s 1 2 Special Relativity and Electromagnetism, USPAS, January 2008     M A F E    r q Momentum conservationlaws s o o u

t m m N C T i h v o l o e e

a t t a r

n a s h 4 l m s l e t e -

i u e n m c

o m n a m t f l o e

o t r

m m i h x g m s e p o y

c m e

r 4 n i o e n s - t e m n

s u t c n s u s o m o t i e m n u o m r s

m n v i

e e s i

e r n

n f

i v c d o s t v u o e

c a d b m n

o 4 r u s n i -

e i a t m s s

r n e

m c v r o c o v e m e a n e d

s d w s e s e n

e r i s v t

u g

e n e m d o t t

( m a s s

i s

f o r m

o f

e n e r g y ) ! ! ! 1 3 Special Relativity and Electromagnetism, USPAS, January 2008 F      i n o C L I I I T T a n n n Particle p a e h w l

b p n l t t g e y o h h o o

t e q

r e e r s

n p e u a

i e L C a t

t a o e r r o F M n a , f t r

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l t t

y c M w i o F t l

t , e y F collisions e

a a s w r

s l

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h s e e m a

a n

F v h v e e r e a e a

r ( v g

m L e e y q F

u ) i

s : ( a

on E l i

M s r c m

e e i . n

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a : m a

r V r

t a i i e

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l n s o

t c a m

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e r s e

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e t

o e t q a u l

a e l n

a e n r g d y

i s

E lab 1 . 4 Special Relativity and Electromagnetism, USPAS, January 2008 w e p A

h 2 1 r

o a p . . Particle ontarget

v d p p r e o u 1 1

t w , c o

p i n n i 2 t

g h w p

1 t 0 i w

t c

h v o o

e l e

l l p a q i o d n a u c e r d i a t t s

l y i

c w a

s l i e n n i s t d

h l

W a

o a b p 1 n

f p a

r a o a n n m s d v t i i

t e W - e s p .

v . r 2 collidingparticles

o e w l t o o i t c n h i

t p

i m a e 2 n s

a ( d

s i s n a s m

l M W p a e 1 b W 2 W

r f 1 e r s a t m W e ﬁ c p E m o x x r a e 2 p l o e s a p l i d e d s i 1 e d s r u

t i i m

c a m n p t r g i 0 a g e o )

r n e , b n t t t i e s c o a l n e m s

t h a n p W 1 p 2 5 1 2 Special Relativity and Electromagnetism, USPAS, January 2008   j ρ B E

= = =

c m e g M d A u h l r Maxwell e e y a a r c a c e g n r n c t g n n x r e e a e t i e w

c r

l t d m d e

i a f e c e e r i t n

n i e magnetic monopoles magnetism Gauss lawfor f l a e c s l l s l d i u d t density ofthesources. electric fieldgivesthe Gauss law ’ s i t t s o x y

b r

d e n

y e

q p

n t

h h s c

i h a y

i p : ’

i r [ thereareno o [ [ [ : c A s V/ T C r g divergenceofthe n s e ] / / e Equations : m m m s s

d e a 2 3 ] r ] ]

n n e e s l c d a c e

t r c

e o i u p

f E r

t e r l i e e o l e n c in theloop(staticelectricfield) field inclosedloopproportionalto current flowing Ampere-Maxwell n c t t

r t o

ε µ 1 r c d i of changemagneticfield electric fieldincoilequaltonegativerate Faraday 0 f c

o / 0 (

c i

( s c m s ( 2 a p p p

h t = e n e e r a r a

e r i d m ε m g d b r 0

g n u e o M µ t t a f e e ’ i 0 t

b v s i l d a t lawofinduction i i o i i l g t g

c i y n p h t n

t ﬁ o s a )

’ e o f

. s r e =

t f f law t l

i r f i 2 d c e r c . e

e 9 s l ﬁ

e e 9 s : integralofmagnetic

e p 7 s p a l 9 d c a 2 e c 4 s ) e 5

) = 8

= :

8 induced 1

4 . 0 8 π 8 5

m 4 1

0 / 1 s - 0 7

- [ 1

2 C

[

V V -

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A - 1 - ] 1 m - 1 ] 1 6 Special Relativity and Electromagnetism, USPAS, January 2008      V a C t I F F I r M n o n n e o r r

d l s t g a o o n e a r

e x e m m c s o t r w t i h i c d t d n

t i o F G e u n g h e o t a l r a c g

e l s d r i e ’ o u

n a e s d t i

s h

f p d g e e f s r e o

a e c q

t l s y o r t h u a

e e e ’ u e w a a

n s n e

t L t t l

q i i l o

a o n o a c e u w f n o l d r

a s m e

m ,

d t

e n t i s w a o o q p

t a g

n z u e o

a n

s e a n s g o n

e e d t b e a b i t d t c u n o a u

i t o s a c n c t g m f s a k i e s

e n

o ,

n t

i l a o f w n u u

a E G v m e p

/ el a

l a o r b M e r u e b e i d

a c s r t

ﬁ a n s p t

ﬁ o r

i e t r a i n f s l s c

n d o

e t

t d s

q h o c

u e t r A a

d a l m e m a t e i r r a o p n

g p n d e n o s i r t f

e e t a f e ’ t e i n s i n r

c a d e l t

a i v

n a u w l e t l n i c

k t

l o

e r

p w

t t

e s

o n

n t i s a l 1 7 Special Relativity and Electromagnetism, USPAS, January 2008    R n a I F L n   c o o e

c r t l a o m K I e a

c n c e l i t e a r t c e n x i e

g v e r e e o c g n a l t i l r n i e n s e u t a c

r t t i

t s c i e o i a e t c c i h n

t z v L

ﬁ e o a e

e o e r f a r r q g l r l

g n d y e u y p o e n d )

a h i d t s r

t z y m

c p o f s h o a i e n a a r c g n r c

s o e t n g : i

f e w c e e

d m l t l i e i e

t f c h

c o r m

t ﬁ t t r m h i o e i o e c

l v n

t d

p h i ﬁ a n s e e t

g p h f l o d

r l i e r e n s s

p e

u g a n a t s n c h r e e

t e d

t i o o l c

f e

f l

g e o e c e l t

r e t g r

c k o p u t i r m a n i i d c r e

a t t a b i i g c u c n

n l t e c e

n e n e e t o

i ( r t c b g

y u ﬁ t e l d 1 : 8 Special Relativity and Electromagnetism, USPAS, January 2008    u E A e M Electromagnetic waves   l n / e s a i s M c a U ﬁ T x t u t n

e a w s r a

d l m k e w o d r e

e t G e m

e b h a l t a l a h

y e v n a ’ ) u e

i u e g o

s d d

c s s e s n

e u e i

c q l n n c e r s a h u l g a t t c w

i a i o

r t a r A c y r

f r i t t

g b

y m o F w i o

e e a

o p e a n r s d b e a n

v s

t a r d b e a

e e n p a i r ’ y s n s y d g r ,

’

l e t a y s

l a h n d

w , 3 l

e a t o i D w e w c

c r t w i

u a o t t d h a n h y r i v d

r e s n a e e

e n e o ﬂ e i x q n p t v o u s i l g e s a w : a

t c r t v e e e

i ( o e

n d c p n c u c

o t b e r o w l

o r o

: e f f H

r m

e p a r e g t z n r . e t i c 1 9 Special Relativity and Electromagnetism, USPAS, January 2008      w p W F F p e i F d f P a . r Nature ofelectromagneticwaves n a e r r r r r l i e i a r o o o d c o o e . t q

e n h h

m m m ﬁ p p f h u c e

r e a a t o w a e

i l A F G g g w t v o q n d a h a a a u e n a m c s a v r t t e e

y u

i i v a t a e r o n p o o h s d

e l r ω f c a n n e s e a e

a y n w t ’ r

t h y i e t

l d r n g t r i a - ’ e a h t a

t M w

w h v v h

w e n l

a e

a s a s a a v a c l

w x v v n l e v u i w e e g l n e u o r u

g e s m c v l l e

i l a i e t

’ n t r c i y s o s

t l o o h a r f e w

k 2 0 Special Relativity and Electromagnetism, USPAS, January 2008   Bibliography E R       l e e Z C I A & J Z C I A U W l c . n n a D a a . . . . n t t t t

s k k r P P r r

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a a r r s l s e e r E I a e e s n n n o v v m l s ,

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A A

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