Chapter1_Notes_v0

h 13 static and dynamic elds electric eld

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Unformatted text preview: as current is constant, the two will be independent (i.e. dI/dt = 0). • In this situation, electromagnetics divides into: electrostatics and magnetostatics. • The former requires stationary charges (i.e. dq/dt = 0) while the last requires constant currents (i.e. dI/dt = 0). Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors 20 • More general: Dynamics, which deals with time-varying ﬁelds that are caused by time varying currents and charge densities (i.e. dI/dt = 0). • In fact, time varying electric ﬁeld generates a time varying magnetic ﬁeld and vice-versa. • In addition to and µ, we also need a conductivity measured in siemens/meter (S/m) denoted σ . • It describes how “freely” electrons can move around material. • For σ = 0 material is perfect dielectric and for σ = ∞ it is said to be a perfect conductor. • σ, , µ are called constitutive parameters . If constituent parameters are constant throughout the material, it is said to be homogeneous. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors Branch Electrostatics Condition Stationary charges ( ∂q/∂t = 0 ) Magnetostatics Steady currents (∂I/∂t = 0 ) Dynamics Time-varying currents (∂I/∂t = 0) 21 Field Quantities (Units) Elec. ﬁeld intensity E (V/m) Elec. ﬂux density D (C/m2 ) D= E Magnetic ﬂux density B (T) Mag. ﬁeld intensity H (A/m) B = µH E, D, B and H (E, D) coupled to (B, H) Table 2: Branches of electromagnetics Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors 22 1.3. Traveling Waves There are many diﬀerent kinds of waves—mechanical ones are easily observable (like stretched strings). Waves share some common properties: • Moving waves carry energy from one point to another • Waves have velocity, e.g. for EM waves c = 3 × 108 m/s • Some waves are linear, i.e. they do not aﬀect each other when passing through each other, e.g. EM and sound waves. • Waves can be transient (caused by short duration disturbances) or continuous harmonic waves (generated by oscillating source). • A wave is a self-sustaining disturbance of the medium in which it travels. Take Fig. 8 as an example of 1-D wave. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors u Figure 1-9 Figure 8: 1-D wave traveling on a string. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. 23 Electromagnetics I: Introduction: Waves and Phasors Cylindrical wavefront Two-dimensional wave (a) Circular waves 24 Spherical wavefront Plane wavefront (b) Plane and cylindrical waves (c) Spherical wave Figure 9: 2- and 3-D waves. Figure 1-10 Extensions to 2-D and 3-D are shown in Fig. 9. 2-D waves are...
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This note was uploaded on 09/25/2013 for the course ECE 331 taught by Professor Martinsiderious during the Fall '12 term at Portland State.

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