By Henri Lauer, Harry Leonard Brown
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28b and c to derive the expressions of the curl of A in the y − z and z − x planes, respectively. 44 2 Vector Analysis and Coordinate Systems y Ax + D ∂Ax z Δy ∂y C(x + Δx, y + Δy) Ax B(x + Δx, y) x a x Az + T Ax + Az c O Az + Az Ay ∂Az Δy ∂y N(y + Δy, z) y M(y, z) b ∂Az Δx ∂x S(z + Δz, x + Δx) Ax Q(z, x) ∂Ay Δz ∂z P ∂A Ay + y Δx ∂x Ay A(x, y) Ay + ∂Ax Δz ∂z R(z + Δz, x) z Fig. dl = ∂Ay ∂Az − ∂y ∂z y z. 245) MNOP Substituting Eq. 245) and the curl A results in ( S= y z into Eq. 240) and the x-component of ∂Ay ∂Az − .
Two point charges Q1 and Q2 with their separation distance is shown in Fig. 1. The electric force, F12 on a point charges Q2 due to Q1 . Mathematically, Coulomb’s law can be written as F12 = k Q1 Q2 a12 , R12 2 Md. A. 1) 51 52 3 Electrostatic Field F12 Fig. 1 Two point charges with separation distance Q2 aR12 R12 Q1 Fig. 2 Two point charges with separation distance F12 Q2 a12 R12 Q1 F21 r1 r2 Origin where Q1 , Q2 are the positive or negative charges in Coulomb (C), R12 is the separation distance in meters, 1 k = 4πε is the proportionality constant.
2. Hayt WH Jr, Buck JA. Engineering electromagnetics. 7th ed. Columbus: McGraw-Hill; 2006 (McGraw-Hill International Edition). 3. Bird J. Higher engineering mathematics. 5th ed. Burlington: Elsevier; 2006. 4. Sadiku MNO. Elements of electromagnetics. 5th ed. New York: Oxford University Press; 2011. 5. Marshall SV, Skitek GG. Electromagnetic concepts and applications. 3rd ed. Upper Saddle River; Prentice Hall; 1990. 1 Introduction In Chap. 1, the basic definition of electromagnetic field parameters and their units were discussed.
Radio engineering principles by Henri Lauer, Harry Leonard Brown