By J.E. Parton
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Translated and revised from the 1986 Russian version.
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Extra resources for Applied Electromagnetics
2 Current from an extensive. charged body. The current or charge per second diverging fr9lI1 a unit volume is equal to the time rate of decrease of charge per unit volume. This equation states that there should be no accumulation of charge and is of great importance in semiconductordevice theory where it is used to describe the variation in time of the charge-carrier density within a particular volume element. 3 Metallic conductors In a metal there are many valence electrons which may be moved through the material under the action of an electric field.
3 Field due to a surface charge Ps coulombs/m 2 The electric fteld strength at any point P due to such a surface S may be found by integration E= J surface Ps dS ,1_ 2 ar "t'l1;EOr where or is a unit vector along r, the position vector of P with respect to dS. If we have a choice of axes these can be ftxed so that the charged surface lies in the yz plane. The point P can be on the x axis, that is coordinates (a, 0, 0). 5b. 5 (a) Surface in yz plane. (b) Infinitely long pllme. The surface element can be an infinite strip dy wide having PL = Ps dy.
The amount of flux is given by the surface integral above and a similar situation occurs in fluid mechanics where the amount of fluid leaving a surface is given by the surface integral of the fluid flow density. --I I I • P O~--------------------------------X z Volume element in an electric field. 12 Consider a volume element in an electric field. 12. At the central point P (x, y, z) Dx , Dy. Dz are all functions of the position coordinates x, y, z and vary accordingly. The surface integralpsD .