Electromagnetic Field Theory: A Problem Solving Approach Part 28 ppsx

... 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...

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...

Ngày tải lên: 03/07/2014, 02:20

... 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 o...

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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...

Ngày tải lên: 03/07/2014, 02:20

... 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...

Ngày tải lên: 03/07/2014, 02:20

... 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 the...

Ngày tải lên: 03/07/2014, 02:20

... 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 ... e-" ' 4, e-'ix" +4, e-i.,x 4, e-i'x (23) Again the phase factors must be equal so that (5) and (6) are again true. Snell's law and the angle o...

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... (35) and (36) for two values of T/7 and see that the quasi-static and transmission line results approach each other as T/r.becomes small. When the roundtrip wave transit ... 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 ar...

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... 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 radiated power ... distribution and calculates the resultant (near and far) fields. If all boundary conditions along the antenna are satisfied, then the solution has been found. Unfor...

Ngày tải lên: 03/07/2014, 02:20

... magnetic scalar potential, 365 spherical coordinates, 284 Laplacian of reciprocal distance, 73-74 Larmor angular velocity, 316 Laser, 517 Law of sines and cosines, 41 Leakage flux, ... VfxA+fVxA (V x A) x A = (A V )A - 'V (A . A) Vx (Vx A) = V(V - A) - V A INTEGRAL THEOREMS Line Integral of a Gradient Vf dlI =f(b) -f (a) Divergence...

Ngày tải lên: 03/07/2014, 02:20