Lecture 31 Chapter 34 Electromagnetic Waves Review For an RLC circuit Voltages add up to emf E vR vC vL Maximum current given by Em I Z Impedance defined as Z R X L XC 2 2 Phase constant defined as X L d L 1 XC d C XL XC tan R Review For RLC circuit resonance and the max current I occurs when d For an ac circuit define rms values I V I rms V rms 2 2 1 d LC E rms Average power dissipated to thermal energy Pavg I 2 rms R E 2 Pavg Erms I rms cos Review Transformer 2 coils primary and secondary wound around same iron core Transformation voltage and current are related to ratio of the number of turns in the coils NS VS VP NP NP IS IP NS Equivalent resistance seen by 2 generator R eq NP R NS EM Waves 1 Electromagnetic waves Beam of light is a traveling wave of E and B fields All waves travel through free space with same speed EM Waves 2 Generate electromagnetic EM waves Sinusoidal current in RLC causes charge and current to oscillate along rods of antenna with angular frequency Changing E and B fields form EM wave that travels away from antenna at speed of light c 1 LC EM Waves 3 E and B fields change with time and have features E and B fields to direction of wave s travel transverse wave E field is B field Direction of wave s travel is given by cross product r r E B E and B fields vary Sinusodially With same frequency and in phase EM Waves 4 Write E and B fields as sinusoidal functions of position x along path of wave and time t E E m sin kx t B Bm sin kx t Angular frequency and angular wave number k E and B components cannot exist independently 2 f k 2 EM Waves 5 Speed of wave is v k Using definition of and k velocity is 2 k 2 f 2 f v f k 2 In vacuum EM waves move at speed of light v c f c 3 10 m s 8 EM Waves 6 Use Faraday s and Maxwell s laws of induction r r r r d B d E B ds 0 0 E ds dt dt Can prove that speed of light c is given by proof done inEsection 34 3 1 c m Bm c 0 0 c 3 10 m s 8 Light travels at same speed regardless of what reference frame its measured in EM Waves 7 EM waves can transport energy and deliver it to an object it falls on Rate of energy transported per unit area is given by Poynting vector S and defined as r 1 r r S E B 0 SI unit is W m2 Direction of S gives wave s direction of travel EM Waves 8 Magnitude of S is given by S 1 0 EB Found relation c Em Bm Rewrite S in terms of E since most instruments measure E component rather than B E S E 0 c Instantaneous energy flow rate is 1 S 1 c 0 E 2 EM Waves 9 Usually want time averaged value of S also called intensity I I S energy time power avg I E c 1 2 avg 0 E c 1 area 2 m ave area ave sin 2 kx t avg 0 Average value over full cycle of sin 2 1 2 Em Use the rms value Erms 2 Rewrite average S or intensity as I 1 E 2 0c rms EM Waves 10 Find intensity I of point source which emits light isotropically equal in all directions power energy time I S avg area ave area ave Find I at distance r from source Imagine sphere of radius r and area Power PS I 2 Area 4 r I decreases with square of distance A 4 r 2 EM Waves 11 Checkpoint 2 Have an E field shown in picture A wave is transporting energy in the negative z direction What is the direction of the B field of the wave Poynting vector gives r 1 r r S E B 0 Use right hand rule to find B field Positive x direction
View Full Document
Unlocking...