按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,Short Version:29.Maxwells Equations&EM Waves,短版,:29.,麥克斯韋方程和電磁波,Short Version:29.Maxwell,29.1.The Four Laws of Electromagnetism,電磁學的四個定律,Law,定律,Mathematical,數學,Statement,陳,述,Physical,物理,Meaning,意義,Gauss for,E,E,的高斯,How,q,produces,E,;,q,怎樣產生,E,；,E,lines begin&end on qs.,E,線始和終於,q,。,Gauss for,B,B,的高斯,Faraday,法拉第,Ampere,安培,(Steady,I,only),(,限用於穩,I,),4 Laws of EM(incomplete),電磁學的四個定律,(,不完整,),No magnetic monopole;,無磁單極；,B,lines form loops.,B,線必成圈。,Changing,B,gives emf.,B,變動即產生,emf,Moving charges give,B,.,電荷移動即生,B,。,Note,E,-,B,asymmetry between the Faraday&Ampere laws.,留意法拉第和安培定律間,E,-,B,並不對稱。,29.1.The Four Laws of Electro,29.2.Ambiguity in Amperes Law,安培定律的含糊,B,in a,RC,circuit.,RC,線路中的,B,Amperes law,安培定律,:,I,is current through any open surface,S,bounded by,C,.,I,是通過任何被,C,圍住的開放式表面的電流。,Current flows through surfaces 1,2,&4.,1,2,和,4,面有電流通過。,But not,3,.,3,則沒有。,Amperes law fails(for non-steady current).,安培定律用於非穩定電流時失敗。,Maxwells modification,馬克斯威爾的修正,:,Changing,E,gives,I,which in turn gives,B,.,變動,E,產生,I,，以產生,B,。,位移電流,29.2.Ambiguity in Amperes La,29.3.Maxwells Equations,馬克斯威爾方程式,Law,定律,Mathematical Statement,數學陳,述,Physical Meaning,物理意義,Gauss for,E,E,的高斯,How,q,produces,E,;,q,怎樣產生,E,；,E,lines begin&end on qs.,E,線始和終於,q,。,Gauss for,B,B,的高斯,Faraday,法拉第,Ampere-Maxwell,安培,-,馬克斯威爾,No magnetic monopole;,無磁單極；,B,lines form loops.,B,線必成圈。,Changing,B,gives emf.,B,變動即產生,emf,Moving charges&changing,E,give,B,.,電荷移動和,E,變動都產,生,B,。,Maxwells Eqs(1864).,馬克斯威爾方程式,(1864),Classical electromagnetism.,古典電磁學,29.3.Maxwells Equations馬克斯威,Maxwells Equations in Vacuum真空中的馬克斯威爾方程式,Gauss for,E,E,的高斯,Gauss for,B,B,的高斯,Faraday,法拉第,Ampere-Maxwell,安培,-,馬克斯,Maxwells Equations in Vacuum,29.4.Electromagnetic Waves,電磁波,Electromagnetic(EM)waves,電磁波,Faradays law,法拉第定律：,Ampere-Maxwells law,安培,-,馬克斯威爾定律,：,changing,B,gives,E,.,變,B,生,E,。,changing,E,gives,B,.,變,E,生,B,。,29.4.Electromagnetic Waves電,Plane Electromagnetic Wave平面電磁波,EM wave in vacuum is,transverse,:,E,B,k,(direction of propagation),.,電磁波在真空中是,橫,的：,E,B,k,(,進行方司,),For uniqueness,see Prob 46,唯一性請參考習題,46,。,Sinusoidal plane waves going in,x,-direction:,正弦波朝,x,-,方向走：,Right-hand rule,右手法則,Plane Electromagnetic Wave平面電,Gausss Laws高斯定律,Both,E,&,B,field lines are straightlines,E,和,B,的場線都是直線，,so their flux over any closed surfaces vanish identically.,因此它們通過任何密閉曲面的通量為零。,Hence the Gausss laws are satisfied.,所以兩個高斯定律都滿足。,Plane wave:,平面波：,Gausss Laws高斯定律Both E&B fi,Faradays Law法拉第定律,For loop at,x,of height,h,&width,dx,:,在,x,處長,h,寬,dx,的廻路：,Faradays Law:,法拉第定律：,Faradays law expressed as a differential eq:,法拉第定律以微分方程表示：,Faradays Law法拉第定律For loop at,Ampere-Maxwell Law安培-馬克斯威爾定律,I,=0,Ampere-Maxwell Law:,安培,-,馬克斯威爾定律：,Ampere-Maxwell law expressed as a differential eq:,安培,-,馬克斯威爾定律以微分方程表示：,in vacuum,真空中,For loop at,x,of height,h,&width,dx,:,在,x,處長,h,寬,dx,的廻路：,Ampere-Maxwell Law安培-馬克斯威爾定律I,Conditions on Wave Fields波場的條件,Faradays Law:,法拉第定律：,Ampere-Maxwell Law:,安培,-,馬克斯威爾定律：,For,E,=,E,(,x,t,),j,&,B,=,B,(,x,t,),k,For a plane wave,平面波,Faradays Law:,法拉第定律：,Ampere-Maxwell Law:,安培,-,馬克斯威爾定律：,Conditions on Wave Fields波場的條,29.5.Properties of Electromagnetic Waves,電磁波的性質,speed of wave=,波的速率,.,=speed of light in vacuum,光在真空中的速率,=,c,Maxwell:light is EM wave.,馬克斯威爾：光是一種電磁波,1983:meter is defined so that,c,is exactly 299,792,458 m/s.,1983:,米的定義改成,c,剛好是,299,792,458 m/s,。,Hence,0,=1/(4,c,2,10,7,)C,2,/Nm,2,where,c,=,299,792,458.,因此,0,=1/(4,c,2,10,7,)C,2,/Nm,2,此處,c,=,299,792,458,。,29.5.Properties of Electromag,Example,29.2.Laser Light,雷射光,A laser beam with wavelength 633 nm is propagating through air in the+z direction.,一條波長,633 nm,的雷射光束在空氣中朝,+z,方向進行。,Its electric field is parallel to the,x,axis and has magnitude 6.0 kV/m.Find,它的電場平行於,x,軸，大小則為,6.0 kV/m,。求,the wave frequency,(a),波的頻率，,the amplitude of the magnetic field,and(b),磁場的大小，和,the direction of the magnetic field.(c),磁場的方向。,(a),(b),(c)y axis,軸,.,Example 29.2.Laser Light雷射光,Polarization偏振(極),Polarization,偏振,/,E,.,Radiation from antennas are polarized.,從天線發出的輻射是偏振的,E.g.,radio,TV,.,例：電台，電視，,Light from hot sources are unpolarized.,從熱源發出的輻射無偏振,E.g.,sun,light bulb,例：太陽，燈泡,Reflection from surfaces polarizes.,從表面反射會偏振化。,E.g.,light reflecting off car hoods is partially polarized in horizontal direction.,例：光從車子的引擎蓋反射後會在水平方向偏振化。,Transmission through crystal /some plastics polarizes.,穿透晶體或某些塑料會偏振化。,E.g.,Polaroid sunglasses,例：寶麗來太陽鏡。,Law of Malus,:,馬勒定律,：,Only component of,E,/preferred direction,e,is transmitted.,祇有平行於傳輸軸,e,的,E,分量才能,通