Page 162 - Engineering Electromagnetics, 8th Edition

144 ENGINEERING ELECTROMAGNETICS

Figure 6.1 Two oppositely charged
conductors M 1 and M 2 surrounded by a uniform
dielectric. The ratio of the magnitude of the
charge on either conductor to the magnitude of
the potential difference between them is the
capacitance C.

of the total charge on either conductor to the magnitude of the potential difference
between conductors,

Q
C = (1)
V 0

In general terms, we determine Q by a surface integral over the positive conductors,
and we find V 0 by carrying a unit positive charge from the negative to the positive
surface,

E · dS

S
C = (2)
+
− E · dL
−
The capacitance is independent of the potential and total charge, for their ratio
is constant. If the charge density is increased by a factor of N, Gauss’s law indicates
that the electric flux density or electric field intensity also increases by N,as does the
potential difference. The capacitance is a function only of the physical dimensions of
the system of conductors and of the permittivity of the homogeneous dielectric.
Capacitance is measured in farads (F), where a farad is defined as one coulomb
per volt. Common values of capacitance are apt to be very small fractions of a farad,
and consequently more practical units are the microfarad (µF), the nanofarad (nF),
and the picofarad (pF).