4/12/2018. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105. Plan for Lecture 34: Review radiating systems

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Eustacia Sharp
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1 PHY 7 Eodynams 9-9:5 M MWF On 5 Pan o u : Rvw adang sysms Souon o Maxw s quaons wh sous Tm pod sous Examps //8 PHY 7 Spng 8 -- u //8 PHY 7 Spng 8 -- u Gna vw -- SI uns mosop o vauum om ( P M ): Couombs aw: E / mp-maxws aw: E B Faadays aw: B E No magn monopos: B //8 PHY 7 Spng 8 -- u

2 Fomuaon o Maxw s quaons n ms o vo and saa ponas B B B E E E o E //8 PHY 7 Spng 8 -- u Fomuaon o Maxw s quaons n ms o vo and saa ponas -- onnud E / : / E B //8 PHY 7 Spng 8 -- u 5 Fomuaon o Maxw s quaons n ms o vo and saa ponas -- onnud B E on gaug om -- qu / //8 PHY 7 Spng 8 -- u 6

3 //8 PHY 7 Spng 8 -- u 7 Souon o Maxw s quaons n h on gaug -- onnud : souon o d Foma s unon : Gn d G d G psn x y psn x y //8 PHY 7 Spng 8 -- u 8 Souon o Maxw s quaons n h on gaug -- onnud : souon o d Foma a nny : bounday vaus soop Fo h as o s unon : h om o h Gn Dmnaon o d d G G //8 PHY 7 Spng 8 -- u 9 Foma souon o d : d d Two yps o sysms: Tm hamon sou: ( ) ( ) spha hamon xpanson spha Bss unons Chagd pa wh known ajoy: ( ( )) ( ) q q R énad-wh ponas

4 //8 PHY 7 Spng 8 -- u Summay -- quaon om : Gna / qu : gaug om - - on ( ) / ( ) ( ) / ( ) ( ) ( ) / ( ) ( ) / ( ) x y ( ) ( ) ( ) ( ) ( ) x y //8 PHY 7 Spng 8 -- u Souon o Maxw s quaons n h on gaug -- onnud G / : Souon o d d d //8 PHY 7 Spng 8 -- u Eomagn wavs om m hamon sous ha h onnuy ondon : No Cun dnsy : Chag dnsy : o Fo sou : Gna

5 Eomagn wavs om m hamon sous onnud: d d d d d //8 PHY 7 Spng 8 -- u Radaon om m hamon sous -- Chag dnsy: Pona ds om m hamon sous: k d Cun dnsy: Connuy ondon: k d //8 PHY 7 Spng 8 -- u ẑ ŷ k d k d ˆx ( ) ( ) //8 PHY 7 Spng 8 -- u 5 5

6 Eomagn wavs om m hamon sous onnud: Usu xpanson : k k j k h k Y ˆ Y ˆ Spha Bss unon : Spha Hank unon : ˆ Y k j h k k j k n k d j k h k Y ˆ //8 PHY 7 Spng 8 -- u 6 Eomagn wavs om m hamon sous onnud: Usu xpanson : k k a j k h k Y ˆ Y ˆ Spha Bss unon : Spha Hank unon : ˆ a Y j h k k j k n k k d j k h k Y ˆ //8 PHY 7 Spng 8 -- u 7 Foms o spha Bss and Hank unons: sn x j x x sn x osx j x x x os x j x sn x x x x x hx x x h x x x x h x x x x j (x) j (x) y (x) y (x) //8 PHY 7 Spng 8 -- u 8 6

7 Eomagn wavs om m hamon sous onnud: Y ˆ a k d j k h k Y ˆ ˆ a Y k d j k h k Y ˆ Fo (xn o sou) a k h k d j k Y ˆ kh k d j k Y ˆ //8 PHY 7 Spng 8 -- u 9 Eomagn wavs om m hamon sous onnud -- som das: k ˆ d j k h k Y w k h ( k) d m( ) j ( k ) j ( k) d m( ) h ( k ) h ( ) d ( ) Y ( ) no ha o R wh ( ) k h ( k) d( ) j ( k) Sma aonshps an b wn o a and. ˆ ẑ R ˆx ŷ //8 PHY 7 Spng 8 -- u Eomagn wavs om m hamon sous onnud: Fo (xn o sou) a k h k d j k Y ˆ kh k d j k Y ˆ No ha and a onnd va h onnuy ondon: Examp o adaon sou os R / R / R ˆ //8 PHY 7 Spng 8 -- u 7

8 Examp o adaon sou os R / R / R ˆ / R ˆ k d h k jk k R Evauaon o R : / R os d h k jk ˆ k k os R k R k //8 PHY 7 Spng 8 -- u k R k R Examp o adaon sou / R / R ˆ os R / R ˆ k d h k j k ( R k ( R k //8 PHY 7 Spng 8 -- u Examp o adaon sou / R / R ˆ os R k R / R os d h k j k ( ) R k ( ) R k //8 PHY 7 Spng 8 -- u 8

9 Examp o dpo adaon sou -- onnud Evauaon o R : ˆ k k os R k R k k R k R Raonshp o pu dpo appoxmaon (xa whn kr) p 8 R ω d d ˆ Cospondng dpo ds: pω k k ω ˆ p k //8 PHY 7 Spng 8 -- u 5 k 9

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