Electromagnetic Field Theory: A Problem Solving Approach Part 50 pps

... 2 1 dL(x) dx - (- Ao) N 2 1 2 D (18) 2s PROBLEMS Section 6-1 1. A circular loop of radius a with Ohmic conductivity oa and cross-sectional area A has its center a small distance D away from ... circular loop of radius a is a distance D above a point magnetic dipole of area dS carrying a current II. 2 D I 1 dS 468 Electromagnetic Induction...

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...

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 ... 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

... 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

... 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

... magnetic field diffuses into the conductor as a strongly damped propagating wave with characteristic penetration depth 8. The skin depth 8 is also equal to the propagating wavelength, ... to the linear steady-state distribution in (16). Because (14) is a linear equation, for the total solution of the magnetic field as a function of time and...

Ngày tải lên: 03/07/2014, 02:20

... is -J0AAB d +A* A* e -2 1 ' v) dt = (A *,B +ABA*) = I Re (AB*) (62) which is a formula often used for the time-average power in circuits where A and B are the voltage and ... and traveling wave. KO 2 Energy Stored in the Magnetic Field 451 where Ho is the instantaneous magnetic field at t = 0. If the superconducting material has no i...

Ngày tải lên: 03/07/2014, 02:20

... absorption of the polarization along a crystal axis. 5• 0 Electrodynamics-Fiedr s and Waves polarized and the crystal serves as a quarter-wave plate. However, only that ... refracting (birefringent) medium Linearly polarized wave Waves polarized along this axis travel at speed cq Transmission axis Polarizer Figure 7-12 When a linearly polarized wave .....

Ngày tải lên: 03/07/2014, 02:20