Electromagnetic Field Theory: A Problem Solving Approach Part 1 ppsx

... 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 ... If -14 ar r •O r sin 0 a O A 1 (r 1 a( sin OAo) 1 oA* V" -A= (rPA,)+ + r ar r sin 0 ae r sin 0 a4 x 1 a( sin OAs) aA] r sin a8 0 04, a S 1...

Ngày tải lên: 03/07/2014, 02:20

... 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 operation ... 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...

Ngày tải lên: 03/07/2014, 02:20

... 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 ... total charge on the hoop is q = 27taXo so that (14 ) can also be written as qz E.= 4reo (a +z ) 3 / 2 (15 ) When we get far away from the hoop (IzI >...

Ngày tải lên: 03/07/2014, 02:20

... Probkms 12 9 43. 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 ... form Pn =AA n (i) Show that the capacitance is of the form C _2 1 A A 2 What are Co, 6, and A? (j) What is the capacitance when the two spheres are conce...

Ngày tải lên: 03/07/2014, 02:20

... 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

... 0ik (20) 5-8 MAGNETIC FIELDS AND FORCES 5-8 -1 Magnetizable Media A magnetizable medium carrying a free current J 1 is placed within a magnetic field B, which is a function of ... Ax)- B(x). AxAY 1 Ax Ax B.(y +Ay)-Bz(y) . B,(y +Ay)-B(y) ] (2) + AY y A (2) Ay Ay B Y t kx, yl m = iA x Ayi, x Figure 5-26 A magnetic dipole in a magne...

Ngày tải lên: 03/07/2014, 02:20

... situation where e1 = E2 and P 1 #I 2: sin 2 B= 1 tan O8 = (15 ) 1 +A/ II 2 A1 At this Brewster's angle, the reflected and transmitted power flows are at right angles ... critical angle of (17 ), as can be particularly seen when A = -L2 for the magnetic field polarized parallel to the interface or when 81 = e2 for the elect...

Ngày tải lên: 03/07/2014, 02:20

... constants 7= ZoCL and 7 = LL/Zo as the solutions approach the dc steady state. The waveforms begin after the initial V. wave arrives at z = I after a time T= 1/ c. There ... form V+.= AA" (18 ) which when substituted into (17 ) requires AA"-' (A -F, FL) = 0= )A = rjFL (19 ) The total solution is then a sum of the part...

Ngày tải lên: 03/07/2014, 02:20

... Si(x) = 1. 5708 x lim Si(x) - x .2 I x-O 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Figure 9 -13 The sine integral Si(x) increases linearly for small arguments and approaches ir/2 ... for large arguments oscillating about this value for intermediate arguments. 21R /17 L ,2 ( L 1 2 3 kL Figure 9 -14 The radiation resistance for a dipole anten...

Ngày tải lên: 03/07/2014, 02:20

... diode, 19 9 Poisson-Boltzmann equation, 15 7 Polariscope, 518 -520 Polarizability, 14 3 -14 4 and dielectric constant, 14 7 Polarization: boundary conditions, 16 5 -16 6 charge, 14 0 -14 2, 14 9 cylinder, ... 14 9 cylinder, 16 6 -16 8 and displacement field, 14 6 -14 7 electronic, 13 6 force density, 215 - 219 ionic, 13 6 orientational, 13 6 in parallel plate capac...

Ngày tải lên: 03/07/2014, 02:20