Electromagnetic Field Theory: A Problem Solving Approach Part 5 ppsx

... becomes infinitesimally small, each of the bracketed terms defines a partial derivative aA 3A ýAMz lim = ( + + A V (4) ax-o \ax ay az where AV = Ax Ay Az is the volume ... Section 1-3-1 and the vector A: aAx aA, aA, div A = V - A = -+ + (5) ax ay az 1-4-3 Curvilinear Coordinates In cylindrical and spherical coordinates, the divergence...

Ngày tải lên: 03/07/2014, 02:20

... the field plots. Markus Zahn Cartesian Coordinates (x, y, z) af. af af Vf = - , + O i, + i, ax ay Oz aA, aA, aA, V . A= a+ + ax ay az (LAX, A AaA\ .a, O aA. ay z az Ox ... ax ay V2f a& apos; +f + a& apos;f Ox jy az Cylindrical Coordinates (r, 4, z) Of. I af af. Vf = r 4 +• 1 ar r 04 az 1 a 1iA, aA, V * A= - -(rAr)+M +M rr rr a Oz a...

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... incremental line charge alone has a radial field component as given by (5) that in Cartesian coordinates results in x and y components. Consider the line charge dA 1 , a distance ... dis- tance from the infinite sheet. (b) Parallel Sheets of Opposite Sign A capacitor is formed by two oppositely charged sheets of surface charge a distance...

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... A point charge q is placed between two parallel grounded conducting planes a distance d apart. (a) The point charge q a distance a above the lower plane and a distance ... Try power-law solutions q, = AA", b, = Ba and find the characteristic values of A and a that satisfy the equations in (d). (f) Taking a linear combination...

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... A capacitor has a moveable part that can rotate through the angle 0 so that the capacitance C(O) depends on 0. (a) What is the torque on the moveable part? (b) An electrostatic ... charge - Q at radius R 2 . 48. A capacitor C is charged to a voltage V 0 . At t = 0 another initially uncharged capacitor of equal capacitance C is Switc...

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... right-hand side in (12) that accounts for an iron object to be drawn towards a magnet. Magnetiz- able materials are attracted towards regions of higher H. 5- 8-2 Force on a ... the magnetic dipole moment m = i Ax Ay iý: lim f = m [LB +-aB, + B,, (3) A O xL ax x y iy Ampere's and Gauss's law for the magnetic field relate t...

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... e -a The solutions are now nonuniform plane waves, as discussed in Section 7-7. Complex angles of transmission are a valid mathematical concept. What has happened is that ... equal to the angle of reflection while the transmitted angle is given by Snell's law. (a) Electric field polarized parallel to the interface. (b) Magnetic field para...

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... that the quasi-static and transmission line results approach each other as T/r.becomes small. When the roundtrip wave transit time is so small compared to the time scale ... V~L~t) t>T (C) Figure 8-14 (a) A step voltage is applied to transmission lines loaded at z = 1 with a capacitor CL or inductor LL. The load voltage and current are...

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... Figure 9-7e. (c) Arbitrary Current Phase For arbitrary current phase angles and dipole spacings, a great variety of radiation patterns can be obtained, as illus- trated by the ... L Secondary maxima then occur at nearby angles but at much smaller amplitudes compared to the main lobe at 0 = 7r/2. 9-4-3 Radiation Resistance The total time-average rad...

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... 54 0 Inductance: of coaxial cable, 456 - 458 , 57 5 external, 456 - 457 and ideal transformer, 414-4 15 internal, 457 - 458 and magnetic circuits, 407-411 mutual, 398 as quasi-static approximations ... Charge relaxation Transmission coefficient, 52 3 Transmission line: approach to dc steady state, 58 5 -58 9 equations, 56 8 -57 6 losses, 602-603 sinusoidal...

Ngày tải lên: 03/07/2014, 02:20