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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 timevarying 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 viceversa.
• 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 Timevarying
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 selfsustaining disturbance of the medium in which
it travels.
Take Fig. 8 as an example of 1D wave.
Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors u Figure 19 Figure 8: 1D 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
Twodimensional wave (a) Circular waves 24 Spherical wavefront Plane wavefront (b) Plane and cylindrical waves (c) Spherical wave Figure 9: 2 and 3D waves. Figure 110 Extensions to 2D and 3D are shown in Fig. 9. 2D 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.
 Fall '12
 MartinSiderious
 Electromagnet

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