Electrostatics

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Field Analysis and Modeling
-Electrostatics Project-

By Popescu Ciprian
FILS, Group 1222E

Index

1. Data of the project
a. Initial values for elements
b. Table with elements and groups of elements
c. Points of measurement
d. Geometric model
2. Changing the polarity of the lower capacitor
3. Test 1. Testing meshes
4. Test 2. Changing the electric permittivity of the dielectric 5. Test 3. Changing the charges of the conductors
6. Test 4. Adding an additional charge between the capacitors 7. Conclusions

The data of the project
The aim of this project is to measure how the change in the electric permittivity of the dielectrics and in the charges of the charges of the conductors affect the electric field strength and the electric potential of the geometric model that is constructed. The initial values of the different parameters are:

* The dielectrics:
* the dielectric block has a relative electric permittivity εr=3 * the air block has a relative electric permittivity εr=1 * The charges of the conductors:
* Conductor c1: 1C= q
* Conductor c2: -1C= -q
* Conductor c3: 1C= q
* Conductor c4: -1C= -q
* The boundary has U=0

The table with elements of the geometry:
Object| Contained elements/labels| Observations|
Vacuum block| Border linesAir block| On the border lines U=0| Auxiliary block| Lines that form the auxiliary square with margin 8 cm| The lines have no property, only to serve in controlling the mesh| | | |

Capacitor 1| Conductors C1 and C2| Contains two blocks of air and 1 block of dielectric| | | |
Capacitor 2| Conductors C3 and C4| Contains two blocks of air and 1 block of dielectric| | | |
Dielectric block| Dielectric material| Has the electric permittivity control property| | | |

In order to see how the variations of these parameters influence the model, the following points were chosen for measurement: * P1(-1.5,0) between the capacitors
* P2(-1.5,1.5) over the bottom plate of the upper capacitor * P3(-1.5,2.25) in the middle of the upper capacitor
* P4(-1.5,3) below the upper plate of the upper capacitor * P5(-1.5,4) over the upper capacitor
* P6(-1.5,-1.5) over the bottom plate of the lower capacitor * P7(-1.5,-2.25) in the middle of the lower capacitor
* P8(-1.5,-3) below the upper plate of the lower capacitor * P9(-1.5,-4) over the lower capacitor
* P10(2.8,0) in the dielectric
* P11(3.2,0) beyond the dielectric
The geometric model
The geometric model designed in QuickField 4.2 is:

In this model, all the conductors have length 3 cm. The starting points are: for C1 (-3,3), for C2 (-3,1), for C3 (-3,-1) and for C4 (-3,-3). All the conductors end at the 0Y axis. The dielectric has a constant width of 1.5 cm and has an initial electrical permittivity of 3 F/m. The outer border is a square of 18 cm which limits the air block and imposes the condition for the electric potential to be 0.

The mesh tests
We will test three meshes, one of about 50 nodes, one of about 100 nodes and one of over 200 nodes in order to prove that the last one is the most accurate and to find the one more appropriate for us. For each mesh we will measure the electric field strength E( in V/m) the electric potential U( in V).

| Mesh1 52 nodes| Mesh2 103 nodes| Mesh3 232 nodes|
Points| | | |
| U (V)| E (V/m)| U (V)| E (V/m)| U (V)| E (V/m)| P1| 3.95E+07| 1.095E+11| 6.727E+07| 7.492E+11| -2.012E+07| 8.612E+11| P2| 7.139E+08| 4.235E+11| -1.583E+08| 1.495E+12| -1.818E+08| 5.946E+11| P3| -2.798E+09| 5.112E+11| -4.420E+09| 5.893E+11| -4.695E+09| 6.119E+11| P4| -7.148E+09| 5.132E+11| -9.053E+09| 6.047E+11| -9.380E+09| 6.356E+11| P5| -1.080E+10| 2.034E+11| -1.510E+10| 4.623E+11| -1.590E+10| 5.670E+11| P6| -5.120E+08| 4.458E+11| -1.375E+08| 1.380E+12...
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