In this information age, from baby monitor to remote-controlledequipment, fromradarto microwave oven,from radiobroadcasttosatelliteTV,from ground mobile communication to space communication, from wireless localarea network to blue tooth technology,andfromglobal positioningto navigation systems,electromagnetic wavesare used as to make these technologies possible.The wirelessinformation highway makes it possible that we canreach anybody anywhere at anytime, and to be able to send textvoice, or video signalsto the recipient miles away.Electromagneticwaves can recreate the experience of events far away, makingpossiblewirelessvirtualrealityTo appreciate the contributions Maxwell and Hertz have made tothe progressof mankind and our culture,one only needs to look atthe wide usage of electromagnetic waves
In this information age, from baby monitor to remote-controlled equipment, from radar to microwave oven, from radio broadcast to satellite TV, from ground mobile communication to space communication, from wireless local area network to blue tooth technology, and from global positioning to navigation systems, electromagnetic waves are used as to make these technologies possible. To appreciate the contributions Maxwell and Hertz have made to the progress of mankind and our culture, one only needs to look at the wide usage of electromagnetic waves. The wireless information highway makes it possible that we can reach anybody anywhere at anytime, and to be able to send text, voice, or video signalsto the recipient miles away. Electromagnetic waves can recreate the experience of events far away, making possible wireless virtual reality
3.Boundary ConditionsforTime-varyingElectromagneticFieldsIn principle, all boundary conditions satisfied by a static field canbe appliedto a time-varying electromagnetic field.(a)The tangentialcomponents of the electric field intensityarecontinuousatanyboundary,i.eenE,t = E2te, ×(E, -E)=0orAs long as the time rate of change of the magnetic flux densityisfinite, using the same method as before we can obtain it from theequation:fE.dl--J.oB.dsSatFor linearisotropic media, the above equation can be rewritten asDit D2t6627
3. Boundary Conditions for Time-varying Electromagnetic Fields In principle, all boundary conditions satisfied by a static field can be applied to a time-varying electromagnetic field. (a) The tangential components of the electric field intensity are continuous at any boundary, i.e. As long as the time rate of change of the magnetic flux density is finite, using the same method as before we can obtain it from the equation: E1t = E2t or en (E2 − E1 ) = 0 S B E dl d = − l S t For linear isotropic media, the above equation can be rewritten as 2 2t 1 1t D D = ① ② en
(b)The normal components of magnetic flux intensityarecontinuousatanyboundaryFrom the principle of magnetic flux continuity, we findBin = B2ne. -(B, -B)=0orForlinearisotropic media, we haveμ,Hin = μ,H2n()The boundary conditionforthe normal components ofelectric flux density depends on the property of the media.In general,from Gauss'lawwe findD2n - Din = Psoren (D, - D)) = Pswhere ps is the surface density of the free charge at the boundary
(b) The normal components of magnetic flux intensity are continuous at any boundary. From the principle of magnetic flux continuity, we find B1n = B2n or en (B2 −B1 ) = 0 (c) The boundary condition for the normal components of electric flux density depends on the property of the media. In general, from Gauss’ law we find D2n − D1n = S or − = S ( ) n D2 D1 e where S is the surface density of the free charge at the boundary. For linear isotropic media, we have 1 H1n = 2 H2n
At the boundary between two perfect dielectrics, because of theabsenceoffreecharges,wehaveDin = D2nFora linearisotropic dielectric,we have8,EI, =8,E2n(d)Theboundary conditionforthe tangentialcomponents of themagneticfield intensity depends also on the property of the mediaIn general, in the absence of surface currents at the boundary, as longas the time rate of change of the electric flux density is finite, we findHit = H2te, ×(H2 -H)= 0orHowever,surface currents can exist on the surface of a perfectelectricconductor,andinthis casethe tangentialcomponents ofthemagnetic fieldintensityarediscontinuous7
At the boundary between two perfect dielectrics, because of the absence of free charges, we have D1n = D2n (d) The boundary condition for the tangential components of the magnetic field intensity depends also on the property of the media. In general, in the absence of surface currents at the boundary, as long as the time rate of change of the electric flux density is finite, we find H1t = H2t or en (H2 − H1 ) = 0 However, surface currents can exist on the surface of a perfect electric conductor, and in this case the tangential components of the magnetic field intensity are discontinuous. For a linear isotropic dielectric, we have 1 E1n 2 E2n =
Assume the boundary is formed by a perfect dielectric and aperfect electric conductor. Time-varying electromagnetic field andconduction current cannot exist in the perfect electric conductor. andthey are able to be only on the surface of the perfect electric conductor.E#0→ J=E→8a↓8H+0→E0E(t), B (t), J (t) = 0→H0J+0The tangential component of the electric field intensityand the normalcomponentof magnetic fieldintensityare continuous at any boundaries.and they cannotexist on the surface ofa perfect electricconductorConseguently,the time-varyingelectricfield must be perpendicularto the surface of the perfect electric conductor, while the time-varyingmagneticfieldis tangentialto the surfaceV
Assume the boundary is formed by a perfect dielectric and a perfect electric conductor. Time-varying electromagnetic field and conduction current cannot exist in the perfect electric conductor, and they are able to be only on the surface of the perfect electric conductor. The tangential component of the electric field intensity and the normal component of magnetic field intensity are continuous at any boundaries, and they cannot exist on the surface of a perfect electric conductor. → E(t), B (t), J (t) = 0 E ≠ 0 → J = E → H ≠ 0 → E ≠ 0 J ≠ 0 → H ≠ 0 Consequently, the time-varying electric field must be perpendicular to the surface of the perfect electric conductor, while the time-varying magnetic field is tangentialto the surface