Charge Distributions and Electric Field Visualization in 3D / lab report

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Question Description

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:

  1. a) Understand the use of coordinate systems to represent 2D Electric Fields,
  2. b) Study the most fundamental charge distribution densities (point, dipole and linear),
  3. 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),
  4. 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,
  5. 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 three- dimensional 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

******se atached file for more info******

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
l.AUJVI d lUI J rt'1' EE Science II Laboratory #04 Charge Distributions and Electric Field Visualization in 3D r 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 I_Al/Vl ' 0 ] B(x,y) - position of particle B [-d/2 , 0 ]=[ .. \') , 0 ] 3. Validate the results using MATLAB - Create a new script in the MATLAB script editor and copy the template below. Make sure to type the equations for the values of QI, Q2, d, A and B. Save the script using the name "EE204_your_last_names_III" and press the run button. Fill Table 6 and compare against Table 5. %------ ------------------------------------------------------------------- % % This simple program computes the Ele c tric Fields due to dipole in a 2-D plane using the Coulomb's Law % %-----------------------------------··------------------------------------- % c l e ar ; cl c ; %-------------------------------------------------------------------------% % SYMBOLS USED IN THIS CODE %-------- -----------------------------------------------------------------% % W = Group number (Assigne d by TA ) % eO free space permittivi ty % er Relative permitt ivi ty Ql = charge I value is stored here % Q2 = charge II va l ue is stored her e % Pi = ? % k = (Coulomb' s c on stant)* (e r ) % Nx = Number of g r id p oints in X-Di r ection % Ny= Numb er o f gr id poin ts in Y-Direction % L = Distance covertu r e % X,Y = coordinat e system % ax,ay = coordi n ates fo r the position of Particle A % bx,by = coordi n ates for the p osit i o n of particle B . % Ra= distance betwee n a selected poin t and the location of part ic le A % Rb= distance betwe e n a selected point and the_location of p articl e B % Ea= [Eax ,E ay] Electric-Field produced by Particle A % Eb = (Ebx,Eby] El e ctric-Field produced by Particle B % %--------------------------------------- ---------------------------------- % % % INITIALIZATION OF INPUT PARAMETERS Here, all the input constants are d ef ined %---- ----------------------- ------------------- -------------------.-- • _ % I W = 3; %Use your group numbe r here . Remem ber to mod i fy b e for e run ni ng che code. eO 8.85*10 A- 1 2 ; er= 1 ; Ql = ; %complete the equation Q2 = ; %complete the equation d = lO*W; A = [ ,O J ; %complete t he equ ation for x compone nt of position vector (Particle A) LdllVldlUJ J tt "-t B = k , OJ ; %comp le t e th e e q uati o n f o r x c ompo ne nt o f po siti o n vec t o r ( Pa rti c l e B, l/ (4*p i *e 0 *e r ); Table 6 - Computed values for charge and position ofparticles A and B (MATLAB) Ql Q2 D - distance between A and B A(x,y} - position of particle A B(x,y} - position of particle B - o .oo~ - (!) · 0 v_ SO ~o (lS;O J (_ - IS 1 o) 4. Plot the electric field - append the next template to your script. Make sure to code the lines for Rb, Eby and the quiver function parameters. Run the code and change the title of the figure to your group number and last names. Save a copy ofthe figure. %------------------------------------------------------------------ ------- i % X Y SYSTEM CALCULATION %-------------------------------------------------------------------------% L = 50 ; Nx = 20; Ny = 20; x = - L: 2 *L/ (Nx - l ) : L; y- - L: 2*L/ (Ny-l ) :L; [X, YJ= me shgr i d (x ,y ) ; Ra = s qrt ( ((X-A ( l ) ) .h 2) +(( Y-A ( 2 ) ).h 2 ) ) ; ·-Rb = ; %compl et e t he equat i on to calculate the d is tance for B %---- -------------------------------------------------------- ----------- --% % CALCULATION OF THE x AN D y COMPONENTS OF TH E ELECTRIC FIELD %-------------------------------------------------------------------------% Ea x (Ql * k .*( X-A ( l )) ) . / (Ra. h3 ) ; Eay (Ql * k .* (Y-A(2)))./(Ra . h3 ) ; Ebx = (Q2* k. * (X-B(l)))./ (Rb. h3 ) ; -Eby = ; %comp l et e the equation to calculat e Y component of B fi e ld %-------------------------------------------------------------------------% % PLOTTING THE ELECTRIC FI ELD %- ----- ---- - - --- -- ----------------- --------------------------- - ----------- % % The fo ll owing l ines are intended to normalize and vi sua liz e the electr i c fiel d % ------ ---- -------------- - --- - - -------Eax . *Ra . Al. 5 ; Eaxl Ea y. *Ra . h l.5; Eay l Ebx l Ebx .*Rb . h l. 5; Eby . *Rb . h l. 5; Ebyl f i gure cont our f (X, Y, ( 1. / Ra. ho. 5 ) + ( 1. / Rb. ho. 5 ), 10 ); colorma p (j et ) ; col o rba r ; t itl e ( ' Cha nge thi s ti tle to your group numbe r and last name s' ) xl abel ( ' x ' ) yl abel ( ' y ' l ho ld on End of fie l d norma l i za t ion ------------------ - -% ------- - -- ---- --q = qui ve r (X, Y , + + ) ; %comple t e (Apply superpos ition o n norma liz ed fiel ds ) q .Col or= ' w' ; ho ld off Observations: The arrows in your MATLAB plot represent the electric field due to the charges and the colored contours represent equipotential surfaces. Identify A and Bin the MATLAB figure. Comment on the field distribution and the equipotential surfaces. Obtain your TA 's signature here after completing Part JU on the first page Part IV: Linear Charge distribution Sometimes, the distances between charges are much smaller than the space from the charges to some point of interest. Under such situations, the system of electric charges is called continuous. That is, the system is equivalent to a total electric charge distribution along a line, surface or volume. The procedure to develop the equations describing this scenario for a line charge is as follow: • We start by considering the electric charge distribution as a set of small elements, each of which contains a small charge ~Q. Here the [X, Y] is the position vector of the evaluation point and [x0 ,y0 J is the position of the dQ element of the rod. The electric field produced by a differential portion of the rod is as follow --+ [ 4Ecx.y) = ,MEx • ] = rx dQ * k * (X - xO) ~------3 +9 2 2 (✓CX- x0) + (Y-y0) ) J dQ * k * (Y - yO) ~---=------=2 2 ( ✓CX-x0) + (Y-y0) ) 3 Next, we substitute the differential charge element by the following equation dQ = dx * l, where dx is a infinitesimal portion of the rod, Ais the lineal charge density and dQ is the electric charge of the infinitesimal portion of the rod . ... 4Ecx,y) • + ydEy = [~ X A*4L*k*(X-x0) ~ - - ~ - - - ~- 3 2 (Y-y0) 2 ) (✓ cx-x0) + ~ A*4L*k*(Y-y0) + y ~--~ ---- 3 ( ✓ CX-x0) 2 + (Y-y0) 2 ) 1 Finally, we evaluate the total field at P(x,y,z) due to the charge distribution. Adding the contributions of all the infinitesimal charge elements (that is, by applying the superposition principle - integration). Ecx.y) = [xEx + yEy] = [x J!:_,/;·dEx + YI!:-l/2 dEyJ (2) 1. Read the situation described below Consider a charged cylinder, C with a length land negligible width (i.e. , approximate the charged cylinder as a line charge distribution with charge density ofvalue rho). _,. Table 7- Equations describing the charge density and lenf!:lh ofthe char!,!ed cylinder ~ rho-Charge density (C/m) (w)(l0-9) / - length of the cylinder (w+ 15) (W = Group number assigned by the TA) Use MATLAB to calculate the total electric field produced by the charged cylinder C by following the steps below: LAUUl4LUIJ f't""t 2. Compute the charge density and length values - open a spreadsheet or use a calculator to calculate rho and /. Complete Table 8 below using the equations in Table 7. Table 8 - Parameters describing the charge density and length of C rho 3 x 10 - e\ \ Cf, 1 3. Validate the results using MATLAB - Create a new script in the script editor and copy the template below. Make sure to type the equations for rho and/. Save the script using the name "EE204_your_last_names_IV" and press the run button. Fill Table 9 and compare against Table 8. %---------------------------- --- ------ ----- -------------- ------------- ---- % % % Th i s program compu t e s t h e El e ct ri c Fi e ld s d ue to a c harg e d r od i n a 2 - D p lane u sing t h e Cou lomb ' s Law %-------------------------------------------- -----------------------------% clear; clc; %------------------------------- --------- ------ --------- -- ------ ---------- % % SYMBOLS US ED I N THI S CODE %---- ---------------- ---------- --- -------------------- ---------- ----- -----% % % % % % W = Gr o up number (As si g n e d by TA) rho = Cha r ge d e n s ity [C/ m] l = le n g t h of C eO = f r ee s pace permi tt i v i ty e r = Re lat i ve p e r mit t i vi t y % d = c h a rge d ensit y f or l in ea r rod % X, Y = c oo r d ina t e system % R = d ist a nce be t ween a s elec ted p oin t a nd t he l o cat i o n of i n finitesimal charge % dE = El ect r ic - Fi el d d u e to in fi n ites i mal cha r ge element I E = Elec t r ic-Field % xO , yO = coo r dinates for the loca t io n of i n f init e simal charge (I nt egration vari a ble) I Pi = ? % k = (Cou l omb ' s con stant)• (e r ) I Nx = Num b er of grid poin t s i n X-Dire ct i on % Ny = Number of grid p oints in Y-D irecti o n L - Distance cover ture %------ - - ------- - --- - ------ - - - - - ----------------- - -- - -- - --------- ----- -- --1 % % INITIALIZATION OF IN PUT PARAMET ERS Her e , all the input c o nstant s are defined %---- -- - - -- - - - -- - -- - - ---- -- - - - - ----- - - -- ---- -- - - - -- ----------------- ------1 w = 5; %Use your group number he::e . Re::-,embe :: to modify before ru nnin g the code' e O = 8 . 85*10~ - 12; er = 1; k = l/(4*pi*e0*er) ; . r ho %complete the equaticn [C/~ J charge density 1 = %complete the equati c n [m 1 length o~ C L-______________----_____ :~SHG~==-~u:::;:._;..:-::o:~ ___ ____ ___________________ ::: L - SO : Nx - 20 ; Ny - 20 ; x- -L : 2 •L/ (Nx - l ) : L; y- - L: 2 ' L/(N y - 1 ) : L; {X,Y J~mes hgr i d ( x , yl ; Table 9 _ Parameters describinf.! the charf.!e densitv and lenJ[th ofC (MA TLAB) C\ rho I s >< \ '1 '0 - JAVVJdl l.ll J rt '-t 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? 10 LAUVJ ,uv• J ,., ... 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 LAIUVI dlVI J tt~ 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. B-eci:21,~ -}-~ ,·~ v l ' ~ fheJtecule.1 A crN;.. w/0 be, n8G)uue_ Si·iy.., --t C'lic, rty wkn -+~ gA f e,hq~-...J ~ e_ I-ea kz,S [-_eM-1 . ( / MJ.S e1>ml ?J..e,y~b(___ m; @c(1) +J.-.e__ M -z....ult., C:6 YYVZ.- c/40 8e.Jr 1--o Vl.o 1.:2Ae.,_ Q)trc(_ clo$f 1" I-<> f ·t.e, e .let#-'(/.¥\ ,·~ Obtain your TA 's signature here after completing Part V on the first page t J II, Df;"b~ t-~ ,t: · SJ i'tJ VL 1 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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