ASSIGN_6d

# ASSIGN_6d - Assignment#6 PHYSICS 354/4-01 ELECTRICITY&...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Assignment #6 PHYSICS 354/4-01 ELECTRICITY & MAGNETISM II April. 2010 Assignment #6 Page 1 of 4 Solution to Assignment # 6 3 7 3 . 9.5, p A travelling wave take the form of ). ( vt z f ± At the interface, ) ( ) ( ) ( 2 1 1 t v g t v h t v g T R I- = +- ..................................................................................(1) Continuity of the slope at the interface: = = = ∂ ∂ = ∂ ∂ + ∂ ∂ z T z I z I z g z h z g . And t f v z f v vt z f t f vt z f z f ∂ ∂- = ∂ ∂ ⇒ - ⋅- ∂ ∂ = ∂ ∂ ⋅- ∂ ∂ = ∂ ∂ 1 ) ( ) ( 1 ) ( t g v v t h t g t g v t h v t g v T R I z T z R z I ∂ ∂ = ∂ ∂- ∂ ∂ ⇒ ∂ ∂- = ∂ ∂ + + ∂ ∂- ∴ = = = 2 1 2 1 1 1 1 1 Integrate w.r.t time, C t v g v v t v h t v g T R I +- =-- ) ( ) ( ) ( 2 2 1 1 1 .........................................................................(2) (1)+(2) C v v v g v v v g C v v v g g v v v C g v v g I T T I T I 2 1 2 2 1 2 1 2 2 1 2 2 2 1 2 2 1 2 +- + = ⇒ + + = + ⇒ + + = ............(3) From (1) C v v v g v v v v g C v v v g v v v g g h I I I I T R 2 1 2 2 1 1 2 2 1 2 2 1 2 2 +- +- =- +- + =- = ............(4) (3) and (4) give the amplitude of the reflected and transmitted wave at any z in terms of the incident wave . 2 8 3 . 9.11, p Given ( ) ( ) b a t r k B t r g t r k A t r f δ ω δ ω +- • = +- • = cos ) , ( and , cos ) , ( . The time average of the product is: ( ) ( ) ∫ +- • ⋅ +- • = ⋅ T a a dt t r k t r k AB T g f cos cos 1 δ ω δ ω . ( ) ) cos( ) cos( 2 1 cos cos sin sin cos cos ) cos( sin sin cos cos ) cos( diff sum Y X Y X Y X Y X Y X Y X Y X + = ⇒ + =-- = + ( ) π ω δ δ δ δ ω δ δ δ δ ω 4 2 ), cos( 2 ) 2 2 sin( 2 ) cos( ) 2 2 cos( 2 =- + + +- • =- + + +- • = ⋅ ∫ T AB t r k T AB dt t r k T AB g f b a T b a T b a b a ) cos( 2 1 b a AB δ δ- = ................................................................................................................................(11a) Using complex notation, ) ( ) ( ) ( * ) ( ) ( ~ ~ ~ ~ b a b a b a i t r k i t r k i t r k i t r k i e AB Be Ae g f Be g Ae f δ δ δ ω δ ω δ ω δ ω- +- •- +- • +- • +- • = • = ⋅ ⇒ = = ........(11b) Comparing (11a) and (11b) ] ~ ~ Re[ 2 1 * g f g f ⋅ = ⋅ 396 . 9.18, p (a) The time constant, , σ ε τ = and , 2 n r = ε shown elsewhere. n = refractive index of the medium....
View Full Document

## This note was uploaded on 12/15/2010 for the course PHYS 354 taught by Professor Josephshin during the Winter '10 term at Concordia Canada.

### Page1 / 4

ASSIGN_6d - Assignment#6 PHYSICS 354/4-01 ELECTRICITY&...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online