Comunicazione elettriche - i campi elettromagnetici

Equazioni di Maxwell

S∂ { }∇ × + =E ( r , t ) B ( r , t ) 0∂t∂ ! "{ }∇ × − =H ( r , t ) D ( r , t ) J ( r , t )∂t ρ∂ ( r , t )∇ ⋅ = −J ( r , t ) ∂td⋅ = − ⋅ ⋅ˆE dl B n dsdtC Sd ! "⋅ − ⋅ ⋅ =ˆH dl D n ds I (t )dtC S d ρ⋅ ⋅ = −ˆJ ( r , t ) n ds ( r , t ) dvdtS V# $ ⋅ ⋅ = ∇ ⋅ˆA n ds AdvS V( )∇ ⋅ ∇ × =A 0% !# % & ⋅ = ∇ × ⋅ ⋅ˆA dl A n dsC S# δ − =f ( x ) ( x x ) dx f ( x )0 0x ∆ →# S 0⋅ ⋅ =ˆA n ds 0 A discontinu o∆S 1' ρ∇ ⋅ = ∇ ⋅ =D ( r , t ) ( r , t ) B ( r , t ) 0⋅ ⋅ = ⋅ ⋅ =ˆ ˆD ( r , t ) n ds Q (t ) B ( r , t ) n ds 0S S( $ε µ= = = + = +D E B H D D P B B M0 0[ ] F{ }+∞ +∞ == ⋅D ( r , t ) dt ' dr ' ( r , r ' ; t , t

' ) E ( r ' , t ' ) 4m secee− ∞ − ∞ % $) { }+∞= ⋅D ( r , t ) dr ' ( r , r ' ; t ) E ( r ' , t )# $ e− ∞* { }+∞) = ⋅D ( r , t ) dt ' ( r ; t , t ' ) E ( r , t ' )% $ e( − ∞# + # ,%τ τ= −(t , ) (t )% # e e0 ρ ρ= −( r , ) ( r )% e e-+ ..ε= ⋅D ( r , t ) ( r , t ) E ( r , t )0 /+1 + 2 + 3 ε=# ( r , t ) ( r , t )e( •0 ε ε ε ε• = = = ( r , t )xx yy zz! ε=D ( r , t ) E ( r , t ) 1 ,0 3σ = ↔ =0 J 0$ c −r r '= < +( r , r '; t , t ' ) 0 t t 'e cµε > >0 0$*# = + JJ ( r , t ) J ( r , t ) J ( r , t ) % 1 + +3c0 0J c 2% d= ⋅ ⋅ˆI (t ) D n ds 4 5D dt Sσ= >J ( r , t ) ( r , t ) E ( r , t ) J ( r , t ) J ( r , t )c C D* τ ε σ=0* 6 1 7 36 σ= → ∞E 00 1 30 4 $⋅ = ⋅

r , t ) 1 r# * ∂ ∂B r t D r t( , ) ( , )[ ]∇ ⋅ × + + ⋅ + = − ⋅E r t H r t H r t E r t J r t E r t E r t J r t( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )c 0∂ ∂t t' 6 ∂ ∂B r t D r t( , ) ( , )+ + ⋅ + = − ⋅S r t dv H r t dv E r t J r t dv E r t dv E r t J r t dv( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )0c∂ ∂t tV V V V V∂ ∂σ 2+ + + =ˆS ( r , t ) nds w (t ) dv E ( r , t ) dv w (t ) dv P (t )0H E∂ ∂t tS V V V+ + + =P t P r t P t P r t P t( ) ( , ) ( ) ( , ) ( )0u H d E+ 0 3# 1 6 ∀ ∈r V #0{ } { }ε=E , B , H , D D E E , B , H , D0 4× = ∀ > ∀ ∈ˆn E r t E t( , ) ( ) t t r V(+ $ T 0=E ( r , t ) E ( r ) × =ˆn H ( r , t ) H (t )00 T=H ( r , t ) H ( r ) ∀ ∈r S00 c 4