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CHAPTER
6
EXPERIMENTAL
MAPPING
METHODS
We have seen in the last few chapters that the potential is the gateway to any
information we desire about the electrostatic field at a point. The path is straight,
and travel on it is easy in whichever direction we wish to go. The electric field
intensity may be found from the potential by the gradient operation, which is a
differentiation, and the electric field intensity may then be used to find the
electric flux density by multiplying by the permittivity. The divergence of the
flux density, again a differentiation, gives the volume charge density; and the
surface charge density on any conductors in the field is quickly found by eval
uating the flux density at the surface. Our boundary conditions show that it must
be normal to such a surface.
Integration is still required if we need more information than the value of a
field or charge density
at a point
. Finding the total charge on a conductor, the
total energy stored in an electrostatic field, or a capacitance or resistance value
are examples of such problems, each requiring an integration. These integrations
cannot generally be avoided, no matter how extensive our knowledge of field
theory becomes, and indeed, we should find that the greater this knowledge
becomes, the more integrals we should wish to evaluate. Potential can do one
important thing for us, and that is to quickly and easily furnish us with the
quantity we must integrate.
Our goal, then, is to find the potential first. This cannot be done in terms of
a charge configuration in a practical problem, because no one is kind enough to
169
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View Full Document tell us exactly how the charges are distributed. Instead, we are usually given
several conducting objects or conducting boundaries and the potential difference
between them. Unless we happen to recognize the boundary surfaces as belong
ing to a simple problem we have already disposed of, we can do little now and
must wait until Laplace's equation is discussed in the following chapter.
Although we thus postpone the mathematical solution to this important
type of practical problem, we may acquaint ourselves with several experimental
methods of finding the potential field. Some of these methods involve special
equipment such as an electrolytic trough, a fluidflow device, resistance paper
and the associated bridge equipment, or rubber sheets; others use only pencil,
paper, and a good supply of erasers. The
exact
potential can never be deter
mined, but sufficient accuracy for engineering purposes can usually be attained.
One other method, called the
iteration
method, does allow us to achieve any
desired accuracy for the potential, but the number of calculations required
increases very rapidly as the desired accuracy increases.
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This note was uploaded on 03/30/2010 for the course EE 2317 taught by Professor Wilton during the Spring '10 term at University of Houston.
 Spring '10
 Wilton
 Electromagnet, Gate

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