《电磁场》课程教学课件（PPT讲稿，英文）Chapter 8 Plane Electromagnetic Waves

The magnetic fieldintensityisH OE.k-Eroe-ike=(1- j)Ere-ke-isouozouu0The amplitude of the magnetic fieldintensity also decreases with z,but the phase is different from that of the electric field intensitySincethe electricandthe magneticEfield intensities are not in phase, thecomplexenergyflowdensityvectorhasnon-zero real and imaginary parts.This means that there is both energyH,flowand energy exchange when a wavepropagatesin a conductive medium.UV

The magnetic field intensity is z E H x y   =  j k z Ex k c j 0 c e − =  k z k z Ex −  −  = − j 0 (1 j ) e e     The amplitude of the magnetic field intensity also decreaseswith z, but the phase is different from that of the electric field intensity. Ex Hy z Since the electric and the magnetic field intensities are not in phase, the complex energy flow density vector has non-zero real and imaginary parts. This means that there is both energy flow and energy exchange when a wave propagates in a conductive medium

Two specialcases:(a) Ifo <<os , as in an imperfect dielectric, the approximationo24~1+08川2aThenk"k'=Vuo2 VsThe electric and the magnetic field intensities are essentiallyinphase. There is still phase delay and attenuationin this case. Theattenuation constantis proportionalto the conductivity (b) If >> o, as in good conductors, we takeO0800u√

Two special cases ： (a) If   , as in an imperfect dielectric,the approximation 2 2 2 1 1 1         +      +     k =     2 k = c   Then Z = The electric and the magnetic field intensities are essentially in phase. There is still phase delay and attenuation in this case. The attenuation constantis proportionalto the conductivity. (b) If , as in good conductors, we take              + 2 1

ouo01Thenfuok=k"The electric and the magnetic field intensities are not in phaseand the amplitudes show a rapid decay due to a large o. In this case,the electromagnetic wave cannot go deep into the medium, and itonly exists near the surface. This phenomenon is called the skineffect.The skin depth Sis the distance over which the field amplitude isreduce by a factor of ! , mathematically determined frome-k's=e-fuoThe skin depth is inversely proportional to the square root of thefrequencyfandtheconductivityo.UV

π 2   k = k = = f     f Z π (1 j) j Then c =  + The electric and the magnetic field intensities are not in phase, and the amplitudes show a rapid decay due to a large . In this case, the electromagnetic wave cannot go deep into the medium, and it only exists near the surface. This phenomenon is called the skin effect. The skin depth  is the distance over which the field amplitude is reduce by a factor of , mathematically determined from e 1 1 e e −  − = k    k πf 1 1 =  = The skin depth is inverselyproportional to the square root of the frequency f and the conductivity 

The skin depths at different frequencies for copper3×1040.051fMHz29.8Smm0.0660.00038The skin depth deceases with increasing frequencyThe frequency for - Isets theSeveralcrossoverfreguencies08boundarybetweenanimperfectfor different materials:dielectric and a conductor, and it isMediaFrequencies MHzcalledcrossoverfrequency2.6Dry Soil(Short Wave)astands for the ratioof6.0Wet Soil(Short Wave)08amplitude of the conduction current0.22Pure Water(Medium Wave)to that of the displacement current.890Sea Water(Super Short Wave)In imperfect dielectrics the dis.15x103Silicon(Microwave)11×104Germanium(Microwave)placementcurrent dominates,whilePlatinum16.9x1016(Light Wave)the converseis true for a good104.4x1016 (Light Wave)Copperconductor.7一

The skin depths at different frequencies for copper 4 f MHz 0.05 1 310  mm 29.8 0.066 0.00038 The skin depth deceases with increasing frequency. The frequency for sets the boundary between an imperfect dielectric and a conductor, and it is called crossover frequency. = 1   stands for the ratio of amplitude of the conduction current to that of the displacement current.   In imperfect dielectrics the dis￾placement current dominates, while the converse is true for a good conductor. Several crossover frequencies for different materials: Media Frequencies MHz Dry Soil 2.6 (Short Wave) Wet Soil 6.0 (Short Wave) Pure Water 0.22 (Medium Wave) Sea Water 890 (Super Short Wave) Silicon 15103 (Microwave) Germanium 11104 (Microwave) Platinum 16.91016 (Light Wave) Copper 104.41016 (Light Wave)

The attenuation of a plane wave is caused by the conductivity o.resulting in power dissipation, and conductors are called lossy mediaDielectrics without conductivityare calledlosslessmediaBesides conductor loss there are other losses due to dielectricpolarization and magnetization. As a result, both permittivity andpermeability are complex, so that = s'- js"and μ = μ' - ju"The imaginary part stands for dissipation, and they are calleddielectricloss and magnetic loss, respectivelyFor non-ferromagnetic media, the magnetization loss can beneglected.For electromagnetic waves at lower frequencies, dielectric loss canbeneglected

The attenuation of a plane wave is caused by the conductivity , resulting in power dissipation, and conductors are called lossy media. Dielectrics without conductivity are called losslessmedia. Besides conductor loss there are other losses due to dielectric polarization and magnetization. As a result, both permittivity and permeability are complex, so that  =  − j and  =  − j. The imaginary part stands for dissipation, and they are called dielectric loss and magnetic loss, respectively. For non-ferromagnetic media, the magnetization loss can be neglected. For electromagnetic waves at lower frequencies, dielectric loss can be neglected