This document describes a laboratory experiment conducted by a student to plot electric and displacement fields using the curvilinear square method for different conductor configurations. In the first part, equipotential lines and flux lines were drawn between two conductors set to 0-60V. The electric field intensity was calculated. In the second part, the capacitance of a coaxial capacitor was calculated theoretically and by plotting field lines, yielding similar results within human and method errors. The purpose of plotting fields graphically and comparing calculations to theory was achieved.

1. UNIVERSITY OF BOTSWANA
FACULTY OF ENGINEERING AND TECHNOLOGY
DEPARTMENT OF ELECTRICAL ENGINEERING
LAB 1: FIELD PLOTTING CURVILINEAR SQUARES
ELECTROMAGNETIC FIELD THEORY
EEB 327
AUTHOR: NTSHOLE B.T
201301848
GROUP B2
DATE OF SUBMISSION: 11/03/2016

2. ABSRACT
The intension of this experiment was to plot E and D for a given configuration of conductor
boundaries using graphical field plotting method known as the curvilinear method. Equipotential
lines and flux lines were drawn at 90degrees keeping the potential difference (Pd) between the
equipotential lines constant. In the second part of the experiment, the potentials at the conductor
boundaries were distinct to be 0 to 60V and the region between the conductor boundaries was
assumed to be filled with air. The magnitude of electric field intensity was calculated using the
following formula for 2mm of radius provided. The formula that was used most of the times to
calculate the estimated electrical field is given below;
𝐸 =
∆𝑉
∆𝐿 𝑁
It was found out that practical and theoretical results were similar, but there were slight
deviations from actual results due to the human errors when plotting as well as insufficient space
for plotting field lines.

3. INTRODUTION
The main objective was to use a graphical field plotting technique to plot an E and D field for a
given configuration of conductor boundaries. Considering the curvilinear method;
Curvilinear method
The procedure was based on the following facts:
 A conductor boundary was an equipotential surface,
 The electric field intensity and electric flux density were both perpendicular to the
equipotential surfaces
 E and D were perpendicular to the conductor boundaries and possess zero tangential
values
 The lines of electric flux begun and terminated on the charge which resulted in a charge-
free homogenous dielectric which begun and terminated only on the conductor
boundaries.
The implications of these statements were considered by drawing streamlines on the sketch
showing equipotential surfaces.
Figure 1: (a) Sketch of the equipotential surfaces between two conductors. The increment of potential
between each of the two adjacent equipotentials is the same.(b) One flux line has been drawn from A to A_,
and a second from B to B_.
Source:
[1] H.Hayt, W. (n.d.). Engineering Electromagnetics, page155.
In Figure 1 above, two conductor boundaries are shown and equipotentials were drawn with a
constant potential difference between the lines. These lines were only the cross sections of the
equipotential surfaces which are cylinders. No variations in the direction normal to the surface of
the paper were permitted. The streamline to begin, or flux line, at A on the surface of the more
positive conductor were arbitrarily chosen. It leaves the surface normally and crossed at right
angles the undrawn but very real equipotential surfaces between the conductor and the first
surface shown. The line is continued to the other conductor, obeying the single rule that the
intersection with each equipotential must be square.

4. RESULTS
( 𝑎) 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑝𝑒𝑟 𝑚𝑒𝑡𝑒𝑟 𝑙𝑒𝑛𝑔𝑡ℎ 𝑓𝑜𝑟 𝑓𝑖𝑔𝑢𝑟𝑒 2
𝐶 =
8.854 × 10−12
× 14
3
𝐶 = 41.3187𝑝𝐹
( 𝑏) 𝐸 𝑎𝑡 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡 𝑠𝑖𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 60𝑉 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑖𝑓 𝑖𝑡𝑠 𝑡𝑟𝑢𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 𝑖𝑠 2𝑚𝑚
𝐸 =
∆𝑉
∆𝐿 𝑁
𝐸 =
(60 − 0)
2 × 10−3
𝐸 =
30𝐾𝑉
𝑚
( 𝑐) 𝜌𝑠 𝑎𝑡 𝑡ℎ𝑎𝑡 𝑝𝑜𝑖𝑛𝑡
𝜌𝑠 = 𝜀𝐸
𝜌𝑠 = 8.854 × 10−12
× 30 × 103
𝜌𝑠 =
265𝑛𝐶
𝑚2

5. 𝑐𝑜𝑎𝑥𝑖𝑎𝑙 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑜𝑟
𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
𝐶 =
2𝜋𝜖 𝑂
𝑙𝑛
𝑎
𝑏
𝑤ℎ𝑒𝑟𝑒 𝑎 = 8𝑐𝑚 𝑎𝑛𝑑 𝑏 = 2.5𝑐𝑚 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑟𝑎𝑑𝑖𝑖 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑖𝑟𝑐𝑙𝑒𝑠
𝐶 =
2 × 𝜋 × 8.854 × 10−12
𝑙𝑛
8
2.5
𝐶 = 47.828𝑝𝐹
𝑃𝑟𝑎𝑐𝑡𝑖𝑐𝑎𝑙
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑑𝑟𝑎𝑤𝑖𝑛𝑔
𝐶 =
𝜖 𝑂 𝑁 𝑄
𝑁 𝑉
𝐶 =
8.854 × 10−12
× (
360
12
)
5
𝐶 = 53.124𝑝𝐹

6. DISCUSSION
Both theoretical and practical results were not that much different because this approach lacks
the accuracy of more elegant methods, allows fairly quick estimates of capacitance while
providing a useful visualization of the field configuration. The curvilinear square method
required patience and skill which the writer used to his advantage to get accurate results. The
slight deviation in the results was because of the following reasons:
 insufficient practice on plotting the equipotential lines and flux lines,
 Human error when plotting
 Failing to terminate most field lines and equipotential lines not crossing over them by 90
degrees.
CONCLUSION
The purpose of this experiment was achieved which was to plot E and D for a given
configuration of conductor boundaries. It was accomplished because results generated in this
report satisfy the objective of this experiment. The capacitance calculated from the drawing was
found to be 𝟓𝟑. 𝟏𝟐𝟒𝒑𝑭 that wasn’t different from the theoretical capacitance which was found to
be𝟒𝟕. 𝟖𝟐𝟖𝒑𝑭. The capacitance per meter length for figure 2 (on appendices) obtained was not
accurate because the author had human errors mostly on field lines not making 90 degrees with
the equipotential lines hence the capacitance per length was affected and was found to be
𝟒𝟏. 𝟑𝟏𝟖𝟕𝒑𝑭.
REFFERENCES
- H.Hayt, W. (n.d.). Engineering Electromagnetics, pages 162 to 168
- Essential electromagnetism.(pdf), pages 74-77.

7. APPENDICES
Figure 2
Figure 3