ECE 305 Electromagnetic Theory Fall 2016 ECE 305 Electromagnetic Theory Part 4: Waves and Applications Chapter 9 Maxwell’s Equations Qiliang Li Dept. of Electrical and Computer Engineering, George Mason University, Fairfax, VA

§9.1 Introduction

§9.2 Faraday’s Law Faraday discovered that the induced emf, Vemf (in volts), in any closed circuit is equal to the time rate of change of the magnetic flux linkage by the circuit

§9.2 Faraday’s Law

=

§9.3 Transformer and motional electromotive forces

Stationary loop in time-varying B-field

B. Moving loop in static B Field

C. Moving loop in time-varying field

Example 9.1 (a)

(b) (c)

Method 2 Read example 9.2 and 9.3

§9.4 Displacement Current For static EM field This is incompatible with time-varying condition So

So, the displacement current density

§9.5 Final Form of Maxwell’s Eqs

§9.6 for self-reading Time-varying EM fields: In Summary: Examples:

§9.7 Time-Harmonic Field

The time element Phasor current IS (dropping the time factor) Time-harmonic field

New form of Maxwell’s equations