1. Calculating and displaying the electric field of a single charged particle. r p. q p. r o

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1 Physics 232 Lab 1 Ch 14 Electric Fields f Pint Charges 1 Objectives In this lab yu will d the fllwing: Cmutatinally mdel the electric field f a rtn Cmutatinally mdel the electric field f a dile (tw equal and site charges) Overview Cmutatin / rgramming is ne f the three basic araches (alng with exeriment and thery) we have fr exlring and understanding nature. A cmuter rgram can bring t life bth analytic and nn-analytic mdels, thereby affrding greater insight. S, a significant cmnent f ur Lab activities this semester will be wrking n and with cmuter mdels. 1. Calculating and dislaying the electric field f a single charged article ŷ r r E ( r ) r 0 xˆ ẑ Thery If a article with charge q is at sitin r, then its electric field at bservatin lcatin r is E r 1 4 q rˆ 2 0 r 4 where r r r r is the distance frm rtn t bservatin lcatin, and rˆ r / r is the unit vectr inting in that directin. The secnd frm (with r 3 in the denminatr) is equivalent but ften handier. If the article has a net sitive charge, the electric field vectr ints frm the surce charge tward the bservatin lcatin (arallel t rˆ ); if the article has net negative charge, the electric field vectr ints frm the bservatin lcatin tward the surce charge (anti-arallel t rˆ ). While the calculatin is straightfrward and can be dne with encil and aer, if yu wish t visualize the electric field thrughut a regin f sace (rather than at just a few ints), it quickly becmes tedius, s a cmutatinal arach (writing a rgram) is an aealing alternative. 1 q 0 r q 3 r,

2 Physics 232 Lab 1 Ch 14 Electric Fields f Pint Charges 2 Prgramming First, yu ll create a simle rgram t visualize a rtn s electric field at just ne bservatin lcatin. Then yu ll extend the rgram t visualize the field at several lcatins at nce. I. Organizatin Yu shuld rganize a rgram in the fllwing way, inserting cmments (##) t exlain what the different sectins f the rgram are ding: First, a sectin giving names t any cnstants that will be used. Secnd, a sectin in which visible bjects like sheres r arrws are created and named. (Smetimes yu will end u creating mre bjects later.) Third, a sectin in which imrtant variables are named and given initial values, if any. Furth, the calculatins. II. A VPythn rgram t calculate the electric field due t a single charged article. II.1. Creating a new rgram file Start a new VPythn rgram by ening VIDLE frm the deskt and saving the rgram as rtn1.y (nte: yu have t tye the.y yurself.) The first tw lines at the very beginning f yur rgram shuld be: frm future imrt divisin frm visual imrt * In the first line nte the tw underscres befre and tw after the wrd future. This makes Pythn treat (1/2) as a flating int number (0.5) instead f an integer (0). After that, lease use a cmment line (starting with ##) t list yur name(s). II.2. Cnstants Cnstants shuld be defined at the beginning f yur rgram. After the lines yu d just written, add: ## cnstants fez = 9e9 #in N m**2 / C**2 qrtn = 1.6e-19 #in Culmbs, charge f a rtn (fez stands fr One Over Fur Pi Esiln-Zer) T make sure yu have tyed everything crrectly, add the statement rint(fez) Run yur rgram by ressing F5 r by using the Run menu. Make sure the crrect value f the cnstant rints ut in the Pythn Shell windw. Nte: Leave the shell windw en (it will autmatically clse when yu clse the editing windw); clsing it can cause errrs when yu run the rgram the next time.

3 Physics 232 Lab 1 Ch 14 Electric Fields f Pint Charges 3 II.3. Objects Add the fllwing tw lines t mark this sectin f the cde fr creating bjects and t create yur charged article. Yu ll want t fill in the blanks s the article is lcated at the rigin and has a radius f meters (an actual rtn is much smaller; exaggerating the size will make it mre visible in the dislay.) ## bjects rtn = shere(s =(,, ), radius =, clr = clr.red) Run the rgram. Yu shuld see a shere in the center f yur dislay windw. If yu dn t see anything, first check the Pythn Shell windw fr errr messages (that s what it s there fr), address them, and then try again. II.4 Initial values f variables In yur rgram add these lines: ## initial values bslc = vectr(2.1e-10, 2.1e-10,0) This marks this sectin f yur cde fr creating and initializing variables and creates the variable bslc, which is shrt fr bservatin lcatin. Yu ll use bslc in yur rgram t reresent the lcatins where yu determine r bserve the electric field. Nte that a vectr such as this is nt a dislayable grahical bject, s it desn t have a s attribute (rather, it can be used t define the sitin f an bject such as an arrw r a shere.) We refer t this vectr simly by its name bslc, whereas the sitin attribute f the dislayable shere bject is a vectr which is referred t as rtn.s. II.5 Calculatins In yur rgram add (and cmlete) the fllwing lines t calculate the electric field at the bservatin lcatin. ## calculatins r = #relative sitin vectr frm rtn t bservatin lcatin rmag = mag(r) #magnitude f relative sitin vectr E = #electric field evaluated at bservatin lcatin Syntax Nte, Exnentials: x n wuld be written x**n T make sure yu ve calculated this rerly, rint the value f the electric field vectr and check it in WebAssign. T visualize the relative sitin vectr, r in the figure at the beginning f this handut, create an arrw whse tail is sitined at the article s sitin and ti extends frm there t the bservatin lcatin. Once yu ve added (and cmleted) the fllwing line f cde, run yur rgram t make sure it des what yu intend.

4 Physics 232 Lab 1 Ch 14 Electric Fields f Pint Charges 4 rarrw = arrw(s =, axis =, clr = clr.green) T visualize the electric field vectr, create an arrw whse tail is sitined at the bservatin lcatin and whse directin and length (axis) are that f the electric field vectr. Once yu ve added (and cmleted) the fllwing line f cde, run yur rgram t make sure it des what yu intend. Earrw = arrw(s =, axis =, clr = clr.range) Yu rbably nticed that Earrw cmletely dwarfs rarrw and the rtn s shere. S that the electric field can be cnveniently visualized in the same sace as the article itself, yu ll want t scale dwn its length. S, yu ll define a cnstant scalefactr ; but first, what s a gd value fr it? The exact value yu chse isn t imrtant, but yu generally want the Electric field vectr t be n the same scale as the relative sitin vectr. S a reasnable value wuld be rmag/mag(e). T determine an arriate value fr scalefactr, temrarily add the fllwing line f cde. rint(rmag/mag(e)) U in the cnstants sectin f yur cde, define scalefactr and give it the value that gt rinted (r any nice, rund value that s in its ball ark.) Once yu ve dne that, feel free t cmment ut r erase the rint statement that yu d added. In the line f cde that defines Earrw, change axis t equal scalefactr*e. Run the rgram t make sure things lk gd (if nt, tweak scalefactr s value until they d.) Save and ulad yur cde. Save a new cy f yur cde as rtn2.y; yu ll mdify this cy t shw the electric field at multile lcatins. II.6 Add mre bservatin lcatins at cnstant distance T see the attern f electric field arund a charged article, yu will extend yur rgram t calculate the electric field at many lcatins, all the same distance frm the surce charge. Frm Phys 231, yu re familiar with using a l t evaluate rerties (sitins, mmenta, and frces) at different times; nw yu ll d smething similar t evaluate a rerty (electric field) at different sitins. Since yu want t evaluate that field at different lcatins with the same distance, yu ll l thrugh different angles, theta, t yur bservatin lcatins. In the cnstants sectin f yur cde, add the fllwing line (analgus t defining yur deltat): deltatheta = i/10 In the initial values sectin f yur cde, add the fllwing line (analgus t starting at t=0)

5 Physics 232 Lab 1 Ch 14 Electric Fields f Pint Charges 5 theta = 0 At the beginning f yur calculatins sectin, add the fllwing tw lines t rehrase the bservatins lcatins in terms f lar crdinates, magnitude and angle. bslcmag = mag(bslc) bslc = bslcmag*vectr(cs(theta),sin(theta),0) T l thrugh angles: Just between these tw new lines add (analgus t while t < max_time:) while theta < 2*i: At the end f the calculatins sectin add (analgus t t = t + deltat) theta = theta + deltatheta S all lines after the while are included in the l, indent all f them (that is, all lines after, but nt including, the while line.) The easiest way is t highlight all f them, then under the Frmat menu, chse indent regin. Finally, cmment ut the rarrw line and save and run yur rgram. Cmare the icture yur rgram generates with that f anther gru (remember, yu may have chsen slightly different scale factrs.) When cnfident that yur rgram is wrking crrectly, save and ulad it. Resave the rgram as rtn3.y; yu ll mdify this cy t shw the electric field at multile distances. II.7 Add mre bservatin lcatins at greater distances T see that its strength drs ff with distance, yu ll need t evaluate the electric field at greater distances frm the rtn. Just as yu nested the calculatin f electric field within a l ver angle, nw yu nest that within a l ver distance. Yu culd use anther while l, but since we ll nly lk at a few distances, a new structure will be handier, a fr l. Relace the bslcmag line with the fllwing fr bslcmag in [mag(bslc),2*mag(bslc),3*mag(bslc)]: Indent all lines belw it (highlight them and frm the Frmat menu select indent regin ) At the bttm, indented nly as far as the while line, add theta = 0 Here s what these changes t yur cde shuld d. First, it sets bslcmag equal t

6 Physics 232 Lab 1 Ch 14 Electric Fields f Pint Charges 6 mag(bslc) and then cycles thrugh evaluating the field at different angles. At the end f that, it resets the angle back t 0, and then changes bslcmag t 2*mag(bslc) and nce again cycles thrugh evaluating the field at each angle, but ut at the new distance. Once it s dne, it resets the angle t zer and reeats the calculatins fr an bservatin lcatin a distance 3*mag(bslc) ut. Save and run yur rgram. Ulad a cy. III. A VPythn rgram t calculate the electric field due t a dile. A dile is a air f equal and site charges, like an electrn and a rtn, a shrt distance aart. Yu ll write a rgram t dislay the ttal electric field (due t bth electrn and rtn) at several lcatins in sace. This can be dne by simly, but carefully, mdifying yur rtn3.y rgram. The dile yu ll mdel cnsists f: a rtn f charge +e lcated at < 4x10-11, 0, 0 > m, reresented by a red shere, and an electrn f charge e lcated at < -4x10-11, 0, 0 > m, reresented by a blue shere. The bservatin lcatins can be the same as in yur rtn3.y rgram. 1. Diagram and lanning Just like when yu re ding an analytical (encil and aer) rblem, yu ll find that a gd diagram reares yu t tackle a cmutatinal rblem. S, n a whitebard, make a careful 2D diagram f the system, in the x-y lane, much like that aearing n the first age f this handut. It shuld include sitin vectrs fr the bservatin lcatin, electrn, and rtn ( r, r e, and r ), relative sitin vectrs frm the charged articles t the bservatin lcatin ( r e and r ), the rtn s cntributin t the electric field at the bservatin lcatin ( E r ), the electrn s cntributin t the electric field at the bservatin lcatin ( E electric field at the bservatin lcatin ( E r E r E r ). e e r ), and the net When yu've gt a cmlete and well labeled diagram, cmare it with that f a neighbring gru 2. Write/Mdify the rgram Yu just wrte a rgram that dislays the electric field due t a single int charge. While yu culd write a new ne frm scratch that des the same fr a dile, I d recmmend ening yur rtn3.y and resaving it as dile.y, and then mdifying it as fllws. In the cnstants sectin, define the charge f the electrn, qelectrn.

7 Physics 232 Lab 1 Ch 14 Electric Fields f Pint Charges 7 In the bjects sectin, mve the rtn frm the rigin t its new lcatin (see abve), and define an electrn laced at the arriate sitin and clred blue. In the calculatins sectin, define the relative sitin frm electrn t bservatin lcatin, re, calculate its magnitude, magre, and use these and qelectrn t find its cntributin t the electric field, Ee. Finally, calculate the ttal electric field, E = Ee + E, and change Earrw t deend n this ttal field rather than just E. It s that simle. Save it, run it, cmare it with that f a neighbring gru, and ulad it when yu re satisfied. Playing arund Yu re dne with the lab, but the fun desn t have t st here. Yu can take hme / yurself / dwnlad frm WebAssign a cy and cntinue laying with it. Here are sme suggestins f things yu might like t try after turning in yur rgram. Add a circle f bservatin lcatins in the xz lane. Make a quadrule ut f tw sed diles, and dislay the electric field. The diles can be aligned n ne axis (+- - +) r they can be laced ne abve the ther, with site rientatins: Yu ll need t increase scalefactr, because the tw diles nearly cancel each ther s fields. In the Visual reference manual available at htt://vythn.rg/cntents/dcs/index.html, in the sectin n Muse Interactins, find ut hw t determine the current sitin f the muse. Dislay the electric field at the muse lcatin, either where yu click the muse, r cntinuusly as yu drag the muse. It s interesting t dislay the electric fields cntributed by each charge, as well as their sum, the net electric field. Mdify a cy f yur rgram s that yu lace a rtn at rest at a lcatin n the +y axis, then release it, and animate its mtin by calculating the electric frce, then alying the mmentum rincile F t t udate the mmentum, then udate f i the sitin, in a l ver time. Nte that in rder t calculate the frce n the rtn yu always have t calculate the electric field f the dile at the current lcatin f the rtn. Try a deltat f arund 1e-17 s, t start with. The trajectry is quite surrising. Think abut whether this trajectry is cnsistent with the Energy Princile. net