Page 161 - Engineering Electromagnetics, 8th Edition

6

CHAPTER

Capacitance

apacitance measures the capability of energy storage in electrical devices.
It can be deliberately designed for a specific purpose, or it may exist as
Can unavoidable by-product of the device structure that one must live with.
Understanding capacitance and its impact on device or system operation is critical in
every aspect of electrical engineering.
A capacitor is a device that stores energy; energy thus stored can either be as-
sociated with accumulated charge or it can be related to the stored electric field,
as was discussed in Section 4.8. In fact, one can think of a capacitor as a device
that stores electric flux,ina similar way that an inductor — an analogous device —
stores magnetic flux (or ultimately magnetic field energy). We will explore this in
Chapter 8. A primary goal in this chapter is to present the methods for calculating
capacitance for a number of cases, including transmission line geometries, and to be
able to make judgments on how capacitance will be altered by changes in materials
or their configuration. ■

6.1 CAPACITANCE DEFINED
Consider two conductors embedded in a homogeneous dielectric (Figure 6.1). Con-
ductor M 2 carries a total positive charge Q, and M 1 carries an equal negative charge.
There are no other charges present, and the total charge of the system is zero.
We now know that the charge is carried on the surface as a surface charge density
and also that the electric field is normal to the conductor surface. Each conductor
is, moreover, an equipotential surface. Because M 2 carries the positive charge, the
electric flux is directed from M 2 to M 1 , and M 2 is at the more positive potential. In
other words, work must be done to carry a positive charge from M 1 to M 2 .
Let us designate the potential difference between M 2 and M 1 as V 0 .We may now
define the capacitance of this two-conductor system as the ratio of the magnitude

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