Download Fundamentals of Electromagnetics: Internal Behavior of by David Voltmer PDF
By David Voltmer
Книга basics of Electromagnetics 1: inner habit of Lumped parts basics of Electromagnetics 1: inner habit of Lumped ElementsКниги Физика Автор: David Voltmer Год издания: 2007 Формат: pdf Издат.:Morgan and Claypool Publishers Страниц: 228 Размер: 1,9 ISBN: 159829170X Язык: Английский0 (голосов: zero) Оценка:Fundamentals of Electromagnetics 1: inner habit of Lumped parts
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Additional resources for Fundamentals of Electromagnetics: Internal Behavior of Lumped Elements
Example text
Substitution of this expression into the dot product, J · ds, provides the required evaluation on the surface. In contrast to line integrals where the initial and final points of integration are quite clear, surface integrals require care in setting the limits of integration. This is easily handled by considering a “test” flux density of unit magnitude that is perpendicular to the surface. The dot product becomes J · ds = 1a N · a N d a = d a; the resulting surface integral is the area of the surface S.
The directed surface element ds = a N d a is the product of two factors—the surface normal vector and the associated differential area. The proper surface normal is defined to be in the direction in which the desired flux is to be calculated. If the direction of the normal is reversed, the sign of dl2 the integral is changed. The convention for closed surfaces is ds that the outward surface normal is chosen so that the inteda gral represents the flux out of the closed surface. The associated differential area is the product of two differential lengths dl1 which lie on the surface S.
More on this will be discussed later. 18-2. A nonuniform current density, J = (sin θ/r 2 )ar , passes through a unit sphere. This current is zero at the poles of the sphere where sin θ = 0 and peaked in the equatorial plane where sin θ = π/2. Calculate the total current outflow. 18-1, but the integrand is complicated by the additional sin θ term; the integral is expressed as π 2π π sin2 θ d θ = (2π ) I= J · ds = = π 2 A. d φ 2 S φ=0 θ=0 Other functional forms for current density are handled in the same manner, though the integrals may not always be as easy to evaluate.