Chapter1_Notes_v0 - Electromagnetics I Introduction Waves...

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Electromagnetics I: Introduction: Waves and Phasors 1 1. Introduction: Waves and Phasors 1.1. Dimensions, units and notation Basis: International System of Units (SI). Table 1 summarizes funda- mental units (note that others can be derived from these): Dimension Unit Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mole mol Table 1: Fundamental SI units. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU.
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Electromagnetics I: Introduction: Waves and Phasors 2 For a range of values from 10 - 18 to 10 18 a set of prefixes is use atto (a), femto (f), pico (p), nano (n), micro ( μ ), milli (m), kilo (k), mega (M), giga (G), tera (T), peta (P), exa (E) which increase by three orders of magnitude. 1.2. Electromagnetism Electromagnetic force is one of the four fundamental forces in na- ture: nuclear, weak-interaction, and gravitational. Gravitational is the weakest at 10 - 41 that of the nuclear force. EM force exists be- tween charged particles . It is the dominant force in microscopic systems (i.e. atoms and molecules). EM force is about 10 - 2 that of the nuclear force. Notation Summary Scalar quantities: Medium weight italic in print and just the letter when written. As in C for capacitance. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU.
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Electromagnetics I: Introduction: Waves and Phasors 3 Units: medium-weight roman letters but looks the same as scalars when written and hopefully obvious from context. Vector quantities: boldface roman in the book as in E for electric field vector. But, when written I will put a little arrow over the letter. Unit vectors: boldface roman with circumflex (hat)ˆover the letter as in ˆ x . Phasors: a tilde˜over the letter as in ˜ E for the phasor quantity of a time-harmonic scalar quantity E ( t ). If it’s a vector phasor it is boldface with a tilde over it. When writing on the board I will try to always use E ( t ) and if I leave off the explicit time dependent ( t ) then a phasor is assumed (an arrow over the top for vector phasor). Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU.
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Electromagnetics I: Introduction: Waves and Phasors 4 Gravitational force analogue Newton’s law of gravity states: F g 21 = - ˆ R 12 Gm 1 m 2 R 2 12 ( N ) (1) which expresses the dependence of the gravitational force F acting on mass m 2 due to a mass m 1 at distance R 12 . (see Fig. 1 ). G is the universal gravitational constant and ˆ R 12 is a unit vector pointing from m 1 to m 2 . m 1 m 2 F g 12 F g 21 R 12 ^ R 12 Figure 1-2 Figure 1: Gravitational forces between two masses. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU.
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Electromagnetics I: Introduction: Waves and Phasors 5 Force acts at a distance concept of fields Each mass m 1 induces a gravitational field Ψ 1 around it so that if another mass m 2 is introduced at some point, it will experience force equal to eq. 1 The field does not physically eminate from the object but its influence exists at every point in space. The field is defined as:
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