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Laboratory #04
EE Science II Laboratory #04
Charge Distributions and Electric Field Visualization in 3D
Summary
In this laboratory experience, you will explore the concepts of charge distributions and electric field distributions
in a 3-dimensional space. You will compute the electric field of various charge geometries (i.e. single charge, dipole
and line distribution). You will use MATLAB as a tool for carrying out the calculations learned during the lab
experience.
During this lab, you will:
a) Understand the use of coordinate systems to represent 2D Electric Fields,
b) Study the most fundamental charge distribution densities (point, dipole and linear),
c) Develop basic skills in the use of MATLAB to compute the electric field produced by a single point charge
confined in an arbitrary volume and compare to the results obtained by two-point charges of opposite charge sign
enclosed in an arbitrary volume (i.e. electric dipole),
d) Develop basic skills in the use of MATLAB to compute the electric field produced by a line with constant charge
along the length (i.e. line charge distribution) and compare to the results obtained in the pre-lab experience,
e) Gain knowledge about uniform electric fields and their applications.
By the end of this experience, you should be able to understand the graphical representation of fields produced
by different electric charge distributions, comprehend the concept of distributed charge in two-dimensional and threedimensional spaces and get a sense of the physical meaning of the electric field.
Objectives
•
Gain an understanding of electric field produced by different charge distributions.
•
Gain proficiency in the use of MATLAB to solve vector field problems.
•
Gain understanding about the concepts of charge distribution, electric field, coulombs law by visualizing
2D and 3D representations of electric fields.
Equipment and Software
•
Advanced Visualization Center
•
MATLAB
University of South Florida
1
EE204-sum.docx
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EE Science II Laboratory #04
Charge Distributions and Electric Field Visualization in 3D
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Printed Name:_
I
I
Bench# Used
Lab Partner:_
Please read the reminder on general policies and sign the statement below. Attach this page
to your Post-Laboratory report.
General Policies for Completing Laboratory Assignments:
For each laboratory assignment, you will also have to complete a Post-Laboratory report. For this report, you are
strongly encouraged to collaborate with your partner and discuss the results, but the descriptions and conclusions must
be completed individually. You will be graded primarily on the quality of the technical content, not the quantity or
style of presentation. Your reports should be neat, accurate and concise (the Summary portion must be less than one
page). Laboratory reports are due the week following the laboratory experiment, unless notified otherwise, and should
be turned in to the TA at the start of the laboratory period. See the syllabus for additional instructions regarding the
report format.
Cheating: Cheating includes improper use of course materials (e.g. old lab reports) acquired from previous semesters
or unauthorized copying among students currently enrolled in the course. University Policies on cheating can be
found in your student catalog. The standard penalty for cheating is an automatic 2-letter reduction in the overall course
grade; however, more severe penalties are possible. Do your own work; discuss the lab concepts with others as
allowed, and learn everything you can.
This laboratory report represents my own work, completed according to the guidelines described above. I have
not improp rly used previous semester laboratory reports, or cheated in any other way.
Signed:-~~ ......:::::,,.....-----------
Please get TA signatures for individual sections below. Please upload this page along with
the post lab report
Part II
Part III
Part IV
PartV
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4. Compute the electric field E - append the followin c d r
.
the Y component of the electric field and run th g ~ e~nes to your ~rtpt. Complete the equation describ ing
number, last names, and the value for/ S
e co e. hange the title of the plot to include your group
· ave a copy of the plot.
:-------------------------------------------------- --- --VARIABLES DECLARATI ON
%
yO = 0 ;
:
---------------- -%
------------------------------------ ------------------ -%
---------------------- -- -------- --------- -----
%---- -- - - CALCULAT ION OF THE:,; AND y COMPONE NTS OF THE ~~~~;;~~-;~~~ ~---- - - %
~~x
: : ((x) (rho*k< (X =: ~~~/~sqrt ( ( (X - x ) . A2 ) + ( (Y - yO) . AZ)). ~;~~ -------------- %
x ) () ./() , %comp lete t he equation
--- . ------------- ----- ----------------------%-------- =~~=~~~~~~-~~-THE:< l\ND y COMPONENTS OF THE-~~~~;;~~-;~~~~ - - --- -%
:-
Y
Ex= ~ntegr al(dEx, - 1/2,1/2, ' Ar r ayVa l ued ' true ~~ -- ------- ------------- - ---- %
Ey = integral (
,
%- -- -------- --- ' , , ' Ar r· ayVa l ued ' ,true);;, i complete
t he e qua tion
---- --- ----------------------------------------- %
%
%-------------
PLOTTING TH E ELECT RI C FI ~LD
:
The following==~==-:==-=~~=~~ =~ -~~-~ ~=~: ::= =-~~~:~~: :~~ ~~~-~ ~~-~~~~;~~~ fi eld
R _= sqrt ( ( (Ex) . A2 ) + ( ( Ey) . A2) ) ;
figure
contourf(X ,Y,R .A 0.5 ,10);
colormap (jet) ;
colorbar;
title('Change
this t·t1
· 1 ude your group number, last names, and the value for 1 used')
xlabel('
x ')
i e t o inc
ylabel ( 'y')
hold on
% --- - ~- -- -- -- ----End of f ield normalizat i on
--- --- --------------qq. =
quiver(X,Y,Ex./(R.
A0.5) ,Ey. /(R . A0.5)); %c omol
Color=,
w, ;
. ete t h e paramet e rs f o r quiver functio n
hold off
5. Compare the electric field for different values of 1- Fill Table 10.
I
l=w
/=w+lOm
/=w+20m
/=w+30m
Table JO - Different values for l
Calculated /
Run your code for each value of 1. Change the title of your plots to include the group number, last names,
and the value for /. Save a copy of all the plots. Compare the plots and provide a brief explanation of your
observation of the electric field.
Observations:
Compare the electric field for different values of/. What happens to the electric field as the length ofthe line
charge distribution increases?
What does the electric field look like
ll
if the observation point is very close to the charge distribution?
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What happens to the electric field as the l approaches irifinity? How is the electric field related to distance from
the line charge distribution for this case? Draw a rough sketch of the Efieldfor this case. (Refer to lecture notes
ifyou do not know the answer).
Obtain your TA 's signature here after completing Part JV on the first page
Part V: Applications of Electrostatics
In this section, you will study an application of electrostatic fields - electrospray ionization. Electrospray ionization
(ESl) is a popular technique for ionizing samples and turning them into a spray or aerosol before their properties are
measured.
1. Understand electrospray ionization -
The following figure shows the basic elements of an ES/ process. The device is composed of an
ionized nozzle, a desolvation gas chamber and a desolvation electrostatic lens. Assume a sample is
composed ofcertain protein compound dissolved in a volatile solvent. The sample enters the nozzle,
ionizing the compound before exiting into the gas chamber. When the ionized spray enters the gas
chamber it is attracted by the electric charge on the electrostatic lens. As the ionized spray
approaches the lens, a flow of nitrogen forces the charges in the molecules closer together
evaporating the solvent that keeps the ions together by capillary forces. The ionized protein
compound is no longer held together by the solvent and the molecules repel each other. This results
in a fine spray at the output of the device. The cross-section of the particle emitter is as shown in
the figure.
0
Gas Chamber
Electrostatic Lens
0
0
0
---- --
0
0
•
.,•
0
•
•
•
Nano flow
capillary
0
Droplet fission
and translation
0
0
0
0
0
High Voltage generat1
Figure - Top and front view of the ES/
11
•
•
4 •
•
•
•
•
•
•
•
•
Individual molecules
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2. Charge polarities for the nozzle - Assume the nozzle is positively charged. Draw the respective sign on the
blue circles to show the potential with respect to ground.
3. Identify the charge of the ionized protein molecules - [ndicate the polarity of the molecules exiting the nozzle.
4. Identify the charge polarity on the lens - Identify the sign of the voltage applied to the lens. Draw the respective
sign in the green circles to show the potential with respect to ground. Hint: The voltage of the lens should be
such that the ionized molecules gets attracted to the output.
5. Explain your observations - Explain the purpose of the N2 gas in the device. Also, explain why drops divide
under the presence of this desolvation gas.
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Obtain your TA 's signature here after completing Part V on the first page
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Laboratory Report
A one paragraph summary of the laboratory assignment.
5 pt
A copy of your MATLAB figures with a one line description for each. Your descri~tion .
should the type of charge distribution and observations on the electric field and eqmpotenttal
surfaces.
4 pt
List other applications of electrostatic forces on electrical engineering.
I pt
{Optional}
Suggestions to improve the laboratory experience.
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