magnitude of the magnetic field must alwaysequal the speed of light.These character-istics of an electromagnetic wave are largelysummarized in the definition of the Poyntingvector which points in the direction of prop-agation and describes how energy propagatesin the wave,vectorS=1μ0vectorE×vectorB.Electromagnetic waves carry energy.Theenergy density of any electric field is given by,uE=12ǫ0E2.The energy density of any magnetic field isgiven by,uB=12B2μ0.So the total energy density of an electro-magnetic wave is given by the sum of thesetwo. For an electromagnetic wave, since the

6–EMwavesandparticles–yeazell–(58010)electricandmagneticfieldsoscillatebothuEExplanation:anduBoscillate.Inthefollowingproblems,consideramonochromatic electromagnetic plane wavepropagating in theydirection.At a par-ticular point in space, the magnitude of theelectric field has an instantaneous value of548 V/m in the positivez-direction.Thewave is traveling in the positivey-direction.yzxEwave propagationμ0= 4π×10−7m·N/A.The Poynting vector isvectorS=1μ0vectorE×vectorB .Fora plane, electromagnetic wave,vectorEandvectorBarealways perpendicular to each other and to thedirection of propagation of the wave; in thiscase, it is in the direction of propagation andhas magnitudeS=E Bμ0=(548 V/m) (1.82793×10−6T)4π×10−7m·N/A=797.133 W/m

Find the instantaneous magnitude of themagnetic field at the same point and time.Thespeedoflightis2.99792×108m/s,thepermeabilityoffreespaceis4π×.015(part3of5)10.0pointsWhat are the directions of the instantaneousmagnetic field and the instantaneous Poynt-ing vector respectively?

What is the instantaneous magnitude of thePoynting vector at the same point and time?Let :μ0= 4π×10−7m·N/A.The Poynting vector isvectorS=1μ0vectorE×vectorB .Fora plane, electromagnetic wave,vectorEandvectorBarealways perpendicular to each other and to thedirection of propagation of the wave; in thiscase, it is in the direction of propagation andhas magnitudeS=E Bμ0=(548 V/m) (1.82793×10−6T)4π×10−7m·N/A=797.133 W/m

2.015(part3of5)10.0pointsWhat are the directions of the instantaneousmagnetic field and the instantaneous Poynt-ing vector respectively?