Electromagnetic Field Theory: A Problem Solving Approach Part 52 pot

... and their magnetic fields. Until Faraday showed that a time varying magnetic field generates an electric field, it was thought that the electric and magnetic fields were ... supposition. It remained for James Clerk Maxwell to show that Fara- day's hypothesis was correct and that without this correction Ampere's law and conservation of c...

Ngày tải lên: 03/07/2014, 02:20

... Losses 525 7.7 UNIFORM AND NONUNIFORM PLANE WA VES 529 7.7.1 Propagation at an Arbitrary Angle 529 7.7.2 The Complex Propagation Constant 530 7.7.3 Nonuniform Plane Waves 532 7.8 ... so that in later chapters most of our attention can be devoted to the applications of the mathematics rather than to its development. Additional mathematical material...

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... Vector Algebra 9 scalar. If the scalar is negative, the direction of the vector is reversed: aA = aAi. + aA,i, + aA i, 1-2-3 Addition and Subtraction The sum of ... the area of the parallelogram formed with A and B as adjacent sides. Interchanging the order of A and B reverses the sign of the cross product: AxB= -BxA AxB BxA=-AxB Figure ......

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... the radial and 0 directions, but sym- metrically located charge elements at -0 have equal field magnitude components that add radially but cancel in the 0 direction. Realizing ... surface charge show that the electric field is purely radial. (b) Gauss's law applied to concentric cylindrical -surfaces shows that the field inside the surface...

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... their centers a distance D apart as in Figure 2-26. We place a line charge A a distance b, from the center of cylinder 1 and a line charge -A a distance b 2 from the ... 0 plane. If a conductor were placed along the x = 0 plane with a single line charge A at x = -a, the potential and electric field for x < 0 is the...

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... potential must approach that of an isolated point charge. Note that for small r the potential becomes very large and the small poten- tial approximation is violated. (c) ... generalize the results of Section 2.4.6 to include dielec- tric media by again choosing a small Gaussian surface whose upper and lower surfaces of area dS are parallel .....

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... Vo (33) (iwsE 2 + 2 ) (iaEl +1) [b(al +jcee) +a( o'2+jWae 2 )] which gives the interfacial surface charge amplitude as °' = e 2 • 2 I1I = (34) [b (a 1 +jOai1) +a( a-2 +jW6 2 )] As the frequency ... that the dielectric can be modeled as a parallel resistor-capacitor combination, edAz 1 s Cz =z s GAz odAz C is the capacitance per unit length and...

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... charge density on the upper electrode is then ev or(f a) = -eE4.(0 = a) =- ra with total charge per unit length E ev b A( ,b=ea)= ofrT( 4a= a)dr=-Eln Ja a a so that the capacitance ... r 0 a b Figure 4-7 Two conducting planes at angle a stressed by a voltage v have a 4-directed electric field. · 270 Electric Field Boundary Value Problems...

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... Problems 305 These relations are known as the Cauchy-Riemann equations and u and v are called conjugate functions. (c) Show that both u and v obey Laplace's equation. (d) ... surface charge at (c) What is the resistance and capacitance? 10. The potential on an infinitely long cylinder is constrained to be V(r = a) = Vo sin n6 -Vo/2 Vo/2...

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... variable in (44), (48) integrates to M=- mN -auedu 2a sinh aa -mN N Se"(u - 1) •, 2a sinh a -mN [e-"( -a - 1)- e" (a - 1)] 2a sinh a -mN - [ -a cosh a+ sinh a] a sinh ... the magnetization saturates at M = mN as all the dipoles have their moments aligned with the field. At room temperature, a is typically very small. Usin...

Ngày tải lên: 03/07/2014, 02:20