Lecture Notes on Electromagnetic Waves | PHY 184, Study notes of Geology

Download Lecture Notes on Electromagnetic Waves | PHY 184 and more Study notes Geology in PDF only on Docsity! Lecture 31 Chapter 34 Electromagnetic Waves Review • For an RLC circuit – Voltages add up to emf – Maximum current given by – Impedance defined as – Phase constant defined as LCR vvv ++=E Z I mE= 22 )( CL XXRZ −+= LX dL ω= C X d C ω 1= R XX CL −=φtan 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 ω – Changing E and B fields form EM wave that travels away from antenna at speed of light, c LC 1=ω 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 – E and B fields vary • Sinusodially • With same frequency and in phase BE rr × EM Waves (6) • Use Faraday’s and Maxwell’s laws of induction • Can prove that speed of light c is given by (proof done in section 34-3) • Light travels at same speed regardless of what reference frame its measured in 00 1 εµ =c m m B Ec = smc /103 8×= dt dsdE BΦ−=•∫ rr dt dsdB EΦ=•∫ 00εµ rr 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 • SI unit is W/m2 • Direction of S gives wave’s direction of travel BES rrr ×= 0 1 µ EM Waves (8) • Magnitude of S is given by • Found relation • Rewrite S in terms of E since most instruments measure E component rather than B • Instantaneous energy flow rate is m m B Ec = c EES 0 1 µ = EBS 0 1 µ = 2 0 1 E c S µ =