Page 57 - Engineering Electromagnetics, 8th Edition

CHAPTER 2 Coulomb’s Law and Electric Field Intensity 39

In Section 2.6, we describe how fields may be sketched, and we use the field of
the line charge as one example.

D2.5. Infinite uniform line charges of 5 nC/m lie along the (positive and
negative) x and y axes in free space. Find E at: (a) P A (0, 0, 4); (b) P B (0, 3, 4).
Ans. 45a z V/m; 10.8a y + 36.9a z V/m

2.5 FIELD OF A SHEET OF CHARGE
Another basic charge configuration is the infinite sheet of charge having a uniform
2
density of ρ S C/m . Such a charge distribution may often be used to approximate
that found on the conductors of a strip transmission line or a parallel-plate capacitor.
As we shall see in Chapter 5, static charge resides on conductor surfaces and not
in their interiors; for this reason, ρ S is commonly known as surface charge density.
The charge-distribution family now is complete—point, line, surface, and volume, or
Q,ρ L ,ρ S , and ρ ν .
Let us place a sheet of charge in the yz plane and again consider symmetry
(Figure 2.8). We see first that the field cannot vary with y or with z, and then we see
thatthe y and z componentsarisingfromdifferentialelementsofchargesymmetrically
located with respect to the point at which we evaluate the field will cancel. Hence
only E x is present, and this component is a function of x alone. We are again faced
with a choice of many methods by which to evaluate this component, and this time we
use only one method and leave the others as exercises for a quiet Sunday afternoon.
Let us use the field of the infinite line charge (16) by dividing the infinite sheet
into differential-width strips. One such strip is shown in Figure 2.8. The line charge

Figure 2.8 An infinite sheet of charge in the yz
plane, a general point P on the x axis, and the
differential-width line charge used as the element in

determining the field at P by dE = ρ S dy a R /(2πε 0 R).