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Display Device Lab Dong-A University Electromagnetic Field and Waves Gi-Dong Lee Outline: Electrostatic Field Magnetostatic Field Maxwell Equation Electromagnetic Wave Propagation

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Display Device Lab Dong-A University Vector Calculus Basic mathematical tool for electromagnetic field solution and understanding.

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Display Device Lab Dong-A University Line, Surface and Volume Integral –Line Integral : Circulation of A around L ( ) Perfect circulation : –Surface Integral : Path L Net outward flux of A

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Display Device Lab Dong-A University Volume Integral : Del operator : Gradient Divergence Curl Laplacian of scalar

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Display Device Lab Dong-A University Gradient of a scalar → V1 V2 dV = potential difference btw the scalar field V

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Display Device Lab Dong-A University Divergence, Gaussian’s law It is a scalar field

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Display Device Lab Dong-A University Curl, Stoke’s theorem ds Closed path L

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Display Device Lab Dong-A University Laplacian of a scalar Practical solution method

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Display Device Lab Dong-A University Classification of the vector field

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Display Device Lab Dong-A University Time-invariant electric field in free space Electrostatic Fields

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Display Device Lab Dong-A University Coulomb’s law and field intensity –Experimental law –Coulomb’s law in a point charge Q1Q2 – Vector Force F 12 or F 21 Q1Q2 F21 r1 r2 F12

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Display Device Lab Dong-A University Electric Field E E : Field intensity to the normalized charge (1) r r’ 1 Q R

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Display Device Lab Dong-A University Electric Flux density D Flux density D is independent on the material property ( 0 ) Maxwell first equation from the Gaussian’s law

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Display Device Lab Dong-A University From this From the Gaussian’s law

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Display Device Lab Dong-A University Electric potential Electric Field can be obtained by charge distribution and electric potential E A Q B In case of a normalized charge Q + : work from the outside - : work by itself

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Display Device Lab Dong-A University Absolute potential E r O : origin point Q=1 Second Maxwell’s Equ. From E and V

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Display Device Lab Dong-A University Second Maxwell’s Equ Relationship btn. E and V E 345 3,4,5 : EQUI-POTENTIAL LINE

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Display Device Lab Dong-A University Energy density We

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Display Device Lab Dong-A University E field in material space ( not free space) Material Conductor Non conductor Insulator Dielctric material Material can be classified by conductivity << 1 : insulator >> 1 : conductor (metal : ) Middle range of : dielectric

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Display Device Lab Dong-A University Convection current ( In the case of insulator) –Current related to charge, not electron –Does not satisfy Ohm’s law

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Display Device Lab Dong-A University Conduction current (current by electron : metal)

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Display Device Lab Dong-A University Polarization in dielectric Therefore, we can expect strong electric field in the dielectric material, not current After field is inducedDisplacement can be occurred – Equi-model Q+Q Dipole moment

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Display Device Lab Dong-A University Multiple dipole moments -+ 0 : permittivity of free space : permittivity of dielectric r : dielectric constant

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Display Device Lab Dong-A University Linear, Isotropic and Homogeneous dielectric D E : linear or not linear When (r) is independent on its distance r : homogeneous When (r) is independent on its direction : isotropic anisotropic (tensor form)

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Display Device Lab Dong-A University Continuity equation Q internal time

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Display Device Lab Dong-A University Boundary condition Dielectric to dielectric boundary Conductor to dielectric boundary Conductor to free space boundary

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Display Device Lab Dong-A University Poisson eq. and Laplacian Practical solution for electrostatic field

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Display Device Lab Dong-A University Electrostatic field : stuck charge distribution E, D field to H, B field Moving charge (velocity = const) Bio sarvart’s law and Ampere’s circuital law Magnetostatic Fields

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Display Device Lab Dong-A University Bio-Savart’s law I dl H field Experimental eq. Independent on material property R

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Display Device Lab Dong-A University The direction of dH is determined by right-hand rule Independent on material property Current is defined by Idl (line current) Kds (surface current) Jdv (volume current) Current element I K

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Display Device Lab Dong-A University Ampere’s circuital law I H dl I enc : enclosed by path By applying the Stoke’s theorem

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Display Device Lab Dong-A University Magnetic flux density From this Magnetic flux line always has same start and end point

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Display Device Lab Dong-A University Electric flux line always start isolated (+) pole to isolated (-) pole : Magnetic flux line always has same start and end point : no isolated poles

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Display Device Lab Dong-A University Maxwell’s eq. For static EM field Time varient system

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Display Device Lab Dong-A University Magnetic scalar and vector potentials Vm : magnetic scalar potential It is defined in the region that J=0 A : magnetic vector potential

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Display Device Lab Dong-A University Magnetic force and materials Magnetic force Q E Bu Q Fm : dependent on charge velocity does not work (Fm dl = 0) only rotation does not make kinetic energy of charges change

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Display Device Lab Dong-A University Lorentz force Magnetic torque and moment Current loop in the magnetic field H D.C motor, generator Loop//H max rotating power

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Display Device Lab Dong-A University Slant loop anan B F0F0 F0F0

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Display Device Lab Dong-A University Magnetic dipole A bar magnet or small current loop I m N S m A bar magnetA small current loop

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Display Device Lab Dong-A University Magnetization in material Similar to polarization in dielectric material Atom model (electron+nucleus) IbIb B Micro viewpoint I b : bound current in atomic model

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Display Device Lab Dong-A University Material in B field B

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Display Device Lab Dong-A University Magnetic boundary materials Two magnetic materials Magnetic and free space boundary

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Display Device Lab Dong-A University Magnetic energy

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Display Device Lab Dong-A University Maxwell equations –In the static field, E and H are independent on each other, but interdependent in the dynamic field –Time-varying EM field : E(x,y,z,t), H(x,y,z,t) –Time-varying EM field or waves : due to accelated charge or time varying current Maxwell equations

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Display Device Lab Dong-A University Faraday’s law –Time-varying magnetic field could produce electric current Electric field can be shown by emf-produced field

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Display Device Lab Dong-A University Motional EMFs E and B are related B(t):time-varying I E

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Display Device Lab Dong-A University Stationary loop, time-varying B field

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Display Device Lab Dong-A University Time-varying loop and static B field

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Display Device Lab Dong-A University Time-varying loop and time-varyinjg B field

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Display Device Lab Dong-A University Displacement current → Maxwell’s eq. based on Ampere’s circuital law for time-varying field In the static field In the time-varying field : density change is supposed to be changed

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Display Device Lab Dong-A University Therefore, Displacement current density

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Display Device Lab Dong-A University Maxwell’s Equations in final forms Gaussian’s law Nonexistence of Isolated M charge Faraday’s law Ampere’s law Point formIntegral form

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Display Device Lab Dong-A University Time-varying potentials stationary E field In the tme-varying field ?

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Display Device Lab Dong-A University Poisson’s eqation in time-varying field poisson’s eq. in stationary field poisson’s eq. in time-varying field ? Coupled wave equation

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Display Device Lab Dong-A University Relationship btn. A and V ?

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Display Device Lab Dong-A University → From coupled wave eq. Uncoupled wave eq.

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Display Device Lab Dong-A University Time-harmonic fields Fields are periodic or sinusoidal with time → Time-harmonic solution can be practical because most of waveform can be decomposed with sinusoidal ftn by fourier transform. Im Re Explanation of phasor Z Z=x+jy=r

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Display Device Lab Dong-A University Phasor form If A(x,y,z,t) is a time-harmonic field Phasor form of A is As(x,y,z) For example, if

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Display Device Lab Dong-A University Maxwell’s eq. for time-harmonic EM field Point formIntegral form

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Display Device Lab Dong-A University EM wave propagation Most important application of Maxwell’s equation → Electromagnetic wave propagation First experiment → Henrich Hertz Solution of Maxwell’s equation, here is General case

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Display Device Lab Dong-A University Waves in general form Sourceless 0 u : Wave velocity

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Display Device Lab Dong-A University Solution of general Maxwell’s equation Special case : time-harmonic

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Display Device Lab Dong-A University Solution of general Maxwell’s equation A, B : Amplitude t - z : phase of the wave : angular frequency : phase constant or wave number

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Display Device Lab Dong-A University Plot of the wave E z t 0 0 /2 3 /2 T/2T3T/2 A A

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Display Device Lab Dong-A University EM wave in Lossy dielectric material Time-harmonic field 0

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Display Device Lab Dong-A University Propagation constant and E field If z-propagation and only x component of Es

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Display Device Lab Dong-A University Propagation constant and H field

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Display Device Lab Dong-A University E field plot of example x z t=t 0 t=t 0 + t

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Display Device Lab Dong-A University EM wave in free space

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Display Device Lab Dong-A University E field plot in free space y x z akak aEaE aHaH TEM wave (Transverse EM) Uniform plane wave Polarization : the direction of E field

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Display Device Lab Dong-A University Reference Matthew N. O. Sadiku, “Elements of electromagnetic” Oxford University Press,1993 Magdy F. Iskander, “Electromagnetic Field & Waves”, prentice hall

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