Faculty of Engineering in Foreign Languages
Electrostatics Project
Fundamentals of Electrical Engineering 3
Student’s name: ____________
Group: ___________________
The bar-shaped magnet and the iron casting between glass
1. Purpose:
The problem, with the help of the simulation program QuickField-Student will show us the behavior of two charge
points of opposite sign. Between them there is isolation and they are surrounded by 3 linear floating conductors,
then by a highly conductive dielectric environment and between the dielectric and the boundary, surrounded by
air. (This was the closest I could get to recreating this experiment in 2D and adapting to the fact I cannot overlay
a different dielectric environment, less conductive like glass, between the charge points and the conductive one.
2. Geometry and data:
Problem type: Electrostatics
Model Class: (adapted to) Plane-parallel
Coordinate System: Cartesian
Length Units: Centimeters
Fig. 1: Design of the high-school experiment
Vertex:
• Positive charge q+ = 1 C (Coordinates: (0.75, 0))
• Negative charge q– = 1 C (Coordinates: (-0.75, 0))
Edges:
• “Positive pole”- the 3 red-colored bars: floating conductors
• “Negative pole”- the 3 blue-colored bars: floating conductors
• Boundary: U = 0V
Blocks:
• Air: εair = 1 (The entire surface between the green square and the dark-grey square)
• Dielectric 1: εi = 10 (insulator - “inside of the magnet”)
• Dielectric 2 and 3: εp = εn = 108 (highly conducting dielectric - “positive and negative pole”)
• Dielectric 4: εFe = 103 (conducting dielectric - “inside of the magnet”)
Fig. 2: Actual experimental setup
3. Points of Computation:
P1 (0.75, 0) P2 (1, 0.5) P3 (0, 0.55) P4 (1, 2.5) P5 (-1, - 2.5)
P6 (3, 0) P7 (-3, 0) P8 (0, 2.75) P9 (0, -2.75) P10 (-4.5, 0)
4. Procedure:
First, we will modify the problem, by adjusting to a finer mesh. Then, we will change the electric permittivity of
the 4th dielectric area.
5. Result Tables:
• Table 5.1 will be a Mesh test.
• Table 5.2 will be an Electrical permittivity test.
• Table 5.3 will be a Charge test.
5.1. Mesh test
• Mesh data:
Mesh 1 has aproximately 50 nodes (Manual spacing 1, 2, 4)
Mesh 2 has aproximately 100 nodes (Manual spacing 0.5, 1, 2)
Mesh 3 has aproximately 200 nodes (Manual spacing 0.4, 0.7, 1.5)
q = ± 1C, εair = 1, εi = 10,
εFe = 103, εp = εn = 108 Mesh 1 Mesh 2 Mesh 3
V1 -29188000 -34891000 -36186000
V2 -29188000 -34891000 -36185000
V3 37277 -650310 317530
El. potential
V4 -11026000 -11621000 -12400000
V5 11026000 11516000 12500000
[V]
V6 -17464000 -19965000 -20516000
V7 17464000 19970000 20582000
V8 -111560 -189880 -169490
V9 111560 110430 -73117
V10 4366100 4733400 4746100
E1 0 54616 54596
E2 5.983 x 108 1.2227 x 109 1.6616 x 109
El. Field Strength
E3 1.866 x 109 5.9221 x 109 6.5563 x 109
E4 9.1473 x 108 8.9965 x 108 9.3765 x 108
[V/m]
E5 9.1473 x 108 9.0562 x 108 9.3214 x 108
E6 8.8955 x 108 1.1226 x 109 1.187 x 109
E7 8.8955 x 108 1.1061 x 109 1.933 x 109
E8 7.1468 x 108 9.4308 x 108 1.073 x 109
E9 7.1468 x 108 9.4498 x 108 1.0777 x 109
E10 8.0943 x 108 9.251 x 108 9.52 x 108
• Graphics from Table 5.1:
Mesh 1 – Built mesh Mesh 1 – Electric Potential Mesh 1 – Electric field strength
Mesh 2 – Built mesh Mesh 2 – Electric Potential Mesh 2 – Electric field strength
Mesh 3 – Built mesh Mesh 3 – Electric Potential Mesh 3 – Electric field strength
Legend: Electric Potential Legend: Electric Field Strength
• Conclusions based on Table 5.1:
A finer mesh implies a larger number of nodes. A larger number of nodes leads to a better
approximation of the vector plane. The shapes seem more rounded, more “natural”.
The obtained experimental values are presumed to become closer to the actual values, the more
nodes there are.
5.2. Electrical permittivity test
• Permittivity data:
Since iron casting (or iron powder) is obtained by applying physical and mechanical processes, its permittivity can be
influence, until it gets into this powder-like state. Therefore, one would recommand experimenting by taking into account
different values for the electric permittivity.
Mesh 3
q = ± 1C, εair = 1, εi = 10 εFe = 100 εFe = 103 εFe = 104
εp = εn = 108
V1 -3.4056 x 108 -36186000 -3642400
V2 -3.4056 x 108 -36185000 -3641900
V3 2625300 317530 31801
El. potential
V4 -1.1484 x 108 -12400000 -1250400
V5 1.1615 x 108 12500000 1265200
[V]
V6 -1.91 x 108 -20516000 -2067200
V7 1.9152 x 108 20582000 2073500
V8 -1210400 -169490 -12338
V9 -670570 -73117 -7447.2
V10 44152000 4746100 478890
El
Fi
E1 50346 54596 55051
.
E2 1.5752 x 1010 1.6616 x 109 1.6709 x 108
E3 6.1677 x 1010 6.5563 x 109 6.5979 x 108
E4 8.6618 x 109 9.3765 x 108 94551000
E5 8.6116 x 109 9.3214 x 108 93983000
E6 1.1082 x 1010 1.187 x 109 1.1957 x 108
E7 1.1136 x 1010 1.933 x 109 1.2019 x 108
E8 9.9685 x 109 1.073 x 109 1.859 x 108
E9 9.7535 x 109 1.0777 x 109 1.0861 x 108
E10 8.8514 x 109 9.52 x 108 96002000
• Graphics from Table 5.2:
Permittivity test 1 – Electric Potential Permittivity test 2 – Electric Potential Permittivity test 3 – Electric Potential
Permittivity test 1 – Electric Field Strength Permittivity test 2 – Electric Field Strength Permittivity test 3 – Electric Field Strength
• Conclusions based on Table 5.2
We notice like in previous experiments, that a higher permittivity (which translates into a less
conductivity) results in smaller values for both the electric potential and the electric field strength.
We can notice from the vector field representation how a smaller value for the permittivity
increases the number of field fronts, showing how the energy itself travels more frequently, with
more ease through those particular envirnoments.
By approximating (since their dependency is not fully linear) we notice that they are reverse
proportionate. For example: if the electric potential measured in the same point, reveleas a value
approximately 10 times smaller than its previous measurement, then the electric permittivity must
have gone up approximately 10 times.
Another important affirmation,which must be said is that the „influence” of changing the electric
permittivity in a region „influences” all the region, both prior and later to it.
5.3. Charge test
• Charge data:
Since when I did the experiment i high-school, with different types of magnets, of different strength, as an equivalent, I
thought it might be interessting to see the equivalent of it, in my experimental setup, meaning that i would have to change
the value of the 2 charge points.
Mesh 3
q+ = + 100 C q+ = + 10 -3 C q+ = 1 C
εair = 1, εi = 10, εFe =104
q- = - 100 C q- = - 10 -3 C q- = - 1 C
εp = εn = 108
V1 -3.6424 x 108 -3642.4 -3642400
V2 -3.6424 x 108 -3661.9 -3641900
V3 3180100 31.801 31801
El. potential
V4 -1.2504 x 108 -1250.4 -1250400
V5 1.2651 x 108 1265.2 1265200
[V]
V6 -2.0672 x 108 -2067 -2067200
V7 2.0735 x 108 2073.5 2073500
V8 -1233800 -12.338 -12338
V9 -744640 -7.4468 -7447.2
V10 4788900 478.89 478890
E1 5505100 55.051 55051
E2 1.6709 x 1010 167090 1.6709 x 108
E3 6.5979 x 1010 659790
El. Field Strength
6.5979 x 108
E4 9.4551 x 109 94551 94551000
E5 9.3983 x 109 93983
[V/m]
93983000
E6 1.1957 x 1010 119570 1.1957 x 108
E7 1.2019 x 1010 120190 1.2019 x 108
E8 1.0859 x 1010 108590 1.0859 x 108
E9 1.0861 x 1010 108610 1.0861 x 108
E10 9.6002 x 109 96003 96002000
• Graphics from Table 5.3:
Charge test 1 – Electric Potential Charge test 2 – Electric Potential Charge test 3 – Electric Potential
\
Charge test 1 – Electric Field Strength Charge test 2 – Electric Field Strength Charge test 3 – Electric Field Strength
• Conclusions based on Table 5.3:
We can say for sure from both the values and the vector representation that there is a linear, directly
proportionate relationship between the charge and the electric field strength, but also between the
charge and the electric potential, meaning when the charge in increased ten-fold for example, so
do the values of the electric field strength and the electric potential.
The „shapes” however of the field themselves do not change.
6. Overall conclusions:
During the last 2 months, while solving both the laboratories and working on this project for this particular
class, I have noticed first, how easy it is to notice the relationships between different physical measurements based
on „playing around” in this simulation program. By analyzing the data gathered in the tables, by looking at the
graphical interpretations, one does not need to know all of the the complex equations, that bring together
everything, in order to work with these experimental setups.
It was also made clear to me, that, while a precise and accurate measurement is the desired outcome, there is
value even in slightly off approximations. The information itself contains value, which can either be of use on its
own or can truely shine, when put in comparison with a different set of experimental data.
In conclusion, one can never have enough data to fully guarantee the outcome of an experiment, but one can
gather more than plenty, given a minimum level of knowledge, patience and a good resolve, to come up with a
well prepared hypothesis, or observation, regarding its behavior, thus proving the importance of experimental
data, experimental measurements in the world of research and of science itself.
