1 Maxwells Equations Differential Forms 2 Maxwells Equations

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Maxwell's Equations (Differential Forms) 2

Maxwell's Equations (Integral Forms) 3

6. 8 Boundary Conditions for Electromagnetics 4

6. 8 Boundary Conditions for Electromagnetics 5 Inside a perfect electric conductor (PEC), E = 0, H = 0 in time-varying case. On a perflect electric conductor: En = ρs/ε, Et = 0 Hn = 0, Ht = Js

6. 9 Charge Current Continuity Relation 6 Current I out of a volume is equal to rate of decrease of charge Q contained in that volume: Used Divergence Theorem

Kirchoff's Current Law 7

6. 10 Free Charge Dissipation in a Conductor Question 1: What happens if you place a certain amount of free charge inside of a 8 material? Answer: The charge will move to the surface of the material, thereby returning its interior to a neutral state. Question 2: How fast will this happen? Answer: It depends on the material; in a good conductor, the charge dissipates in less than a femtosecond, whereas in a good dielectric, the process may take several hours. Derivation of charge density equation: Cont.

Solution to Charge Dissipation Equation 9 For copper: For mica: = 15 hours

6. 11 Electromagnetic Potentials 6. 11. 1 Retarded Potentials 10 Static condition Dynamic condition with propagation delay: Similarly, for the magnetic vector potent

6. 11. 2 Time Harmonic Potentials Time harmonic = Sinusoidal (정현파) Also: 11 If charges and currents vary sinusoidally with time: we can use phasor notation: Maxwell’s equations become: with Phasor expression for potentials become: (propation constant; 전파상수)

12 Cont.

13 Cont.

Example 6 -8 cont. 14 Cont.

Example 6 -8 cont. 15

Summary 16