Download Electromagnetics by Edminister, Joseph; Nahvi, Mahmood PDF

By Edminister, Joseph; Nahvi, Mahmood

ISBN-10: 0071831479

ISBN-13: 9780071831475

ISBN-10: 0071831487

ISBN-13: 9780071831482

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57 CHAPTER 3 Electric Field Eϭ ρ s1 ρ ρ an ϩ s2 an ϩ ar 2⑀ 0 2⑀ 0 2π⑀0 r ϭ 6a x ϩ 6a x ϩ 9a x ϭ 21a x V/m ρs2 ρs1 E E E 0 P(2, 0, z) xϭ0 ρ x xϭ4 Fig. 18. As shown in Fig. 3-22, charge is distributed along the z axis between z ϭ Ϯ5 m with a uniform density ρ ϭ 20 nC/m. Determine E at (2, 0, 0) m in Cartesian coordinates. Also express the answer in cylindrical coordinates. dEϭ ⎛ 2 a x Ϫ za z ⎞ 20 ϫ 10Ϫ9 dz (V/m) Ϫ9 2 ⎜ 4π (10 / 36π ) ( 4 ϩ z ) ⎜ 4 ϩ z 2 ⎟⎟ ⎝ ⎠ z 5 dQ ϭ ρ dz R y (2, 0, 0) x dE Ϫ5 Fig.

Even though electric charge in its smallest division is found to be an electron or proton, it is useful to consider continuous (in fact, differentiable) charge distributions and to define a charge density by ρϭ dQ (C/m 3 ) dv Note the units in parentheses, which is meant to signify that ρ will be in C/m3 provided that the variables are expressed in proper SI units (C for Q and m3 for v). This convention will be used throughout this book. With reference to volume v in Fig. 3-3, each differential charge dQ produces a differential electric field dQ aR 4π⑀ 0 R2 dE ϭ P dE R ρ dQ ϭ ρ dv v Fig.

The electric potential between two infinite parallel plates which are 10 cm apart is set to 100 V. Find the electric field in the space between them. 32. An electric potential v(t) ϭ 100 cos(36000π t) is established between two infinite parallel plates which are separated from each other by 1 cm. Find the displacement current in the space between the plates if it is filled with (a) air, (b) a dielectric material with ⑀r ϭ 100. 33. 25 nC/cm3 is uniformly distributed throughout the spherical volume r Ͻ 1 cm.

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Electromagnetics by Edminister, Joseph; Nahvi, Mahmood


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