082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

156 Chapter 4 Coordinate systems
Engineeringapplication4.1
Electrodecoordinates
Often in science and engineering it is useful to place metallic conductors, known as
electrodes, inside a glass container from which air has been evacuated. For example,electricalvalves,
whicharealsoknown asvacuum tubes,areconstructed inthis
manner.Audioamplifiersthatmakeuseofvalvetechnologyhavemadeacomeback
inrecent years. Many musicians prefer the sound they generate.
Figure 4.4 shows two electrodes inside an evacuated glass envelope. State the
coordinates of the four points A,B, Cand D.
y
12
11
10
9
8
7
6
5
4
3
2
1
A
0 1 2 3 4 5 6 7 8 9 10 11 12
D
glass envelope
C
B
x
Figure4.4
Electrode coordinates.
Solution
A has coordinates (4,9).
B has coordinates (9,6).
C has coordinates (8,10).
D has coordinates (8,6).
Tosimulatetheelectricfieldbetweentheseelectrodes,andtoproduceaproperdesign
formanufacture,acomputermodelmaybeused.Suchamodelwouldinvolvetheuse
of mathematical techniques to solve the fields in the space between the electrodes.
However, the user would have to input the shape of the device. Coordinates would
be used to specify exactly where each part of the device is located. The coordinates
could easily be changed in the computer model to test the effects of changing the
sizeandpositionoftheelectrodes.Computermodelsspeedupthedesignprocessby
avoiding the need forearly-stage prototypes.