Chapter1_Notes_v0

So that if another mass m2 is introduced at some

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Unformatted text preview: 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: ˆ Gm1 ψ1 = −R 2 (N/kg ) R (2) ˆ ˆ where R is a unit vector that points radially away from m1 (−R points towards m1 ). • The field is shown in Fig. 2. • How do we find the force if the field is known? ˆ Gm1 m2 Fg21 = ψ1 m2 = −R12 2 R12 Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. (3) Electromagnetics I: Introduction: Waves and Phasors 6 ^ -R ψ1 m1 Figure 1-3 Figure 2: Gravitational field Ψ1 induced by m1 . or, if the force on a test mass m is known, then Ψ= Fg m Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. (4) Electromagnetics I: Introduction: Waves and Phasors 7 • Electric fields This sets the stage for introducing electric field . Unlike the gravity field, its source is not mass, but charge, which can be either positive or negative. Both fields vary inversely with the square of distance. • Charge has a minimum value: one electronic charge (e) and is measured in coulombs (C). • Electron charge magnitude is e = 1.602 × 10−19 (C) (5) • Actually, the charge of an electron is considered negative (as opposed to, e.g., protons) so that electron charge is qe = −e and the proton in qp = e. • Two charges of the same polarity repel each other, while those of opposite polarity attract each other, Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors 8 • The force acts along the lines joining the charges, • The force is proportional to the charges and inversely proportional to the square of the distance between them. These properties summarized into Coulomb’s law: ˆ Fe21 = R12 q1 q2 (N) in free space 2 4π 0 R12 (6) Symbols are similar to the gravity case, except now we have 0 = 8.854 × 10−12 (F/m) which is electrical permittivity of free space and is measured in Farads/meter (F/m). Fig. 3 illustrates the two point charge case. Electrical force also acts over distance and we again define electric field intensity E due to charge q : ˆ E=R q 4π 0 R2 (V/m) in free space as illustrated in fig. 4 for a positive charge Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. (7) Electromagnetics I: Introduction: Waves and Phasors 9 Fe21 +q2 ^ R12 +q1 R12 Fe12 Figure 1-4 Figure 3: Electric forces between two positive point charges in free space. ^ R E +q Figure 1-5 Figure 4: Electric field E due to charge q. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Figure 1-5 Electromagnetics I: Introduction: Waves and Phasors 10 Two important observations regarding charges: 1. Conservation of charge: (net) electric charge can neither be created nor destroyed. Given np positive and nn...
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