Physics 1502: Lecture 2 Today s Agenda

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1 1 Lectue 1 Phsics 1502: Lectue 2 Tod s Agend Announcements: Lectues posted on: HW ssignments, solutions etc. Homewok #1: On Mstephsics this Fid Homewoks posted on Msteingphsics You need to egiste (included in cost of book) Go to msteingphsics.com nd egiste Couse ID: MPCOTE33308 Lbs: Begin in two weeks Tod s Topic : End of Chpte 20 Define Electic Field in tems of foce on "test chge" Electic Field Lines Emple Clcultions Continuous chge distibutions => integte Moving chges: Use Newton s lw Demonsttion of Msteing Phsics

2 Lectue 1 2 Coulomb's Lw q 1 q 2 F 21 SI Units: in metes q in Coulombs F in Newtons F 12 F 12 = 1 4πε 0 q 1 q πε 0 = N m 2 /C 2 Chles Coulomb ( )

3 Lectue 1 3 Electic Fields The foce, F, on n chge q due to some collection of chges is lws popotionl to q: Intoducing the Electic Field: quntit, which is independent of tht chge q, nd depends onl upon its position eltive to the collection of chges. A FIELD is something tht cn be defined nwhee in spce it cn be scl field (e.g., Tempetue Field) it cn be vecto field (s we hve fo the Electic Field) Lectue 2, ACT 1 Two chges, Q 1 nd Q 2, fied long the -is s shown, poduce n electic field E t point (,) = (0,d) which is diected long the negtive -is. Which of the following sttements is tue? d E Q 1 Q 2 () Both chges Q 1 nd Q 2 must be positive. (b) Both chges Q 1 nd Q 2 must be negtive. (c) The chges Q 1 nd Q 2 must hve opposite signs.

4 Lectue 1 4 How Cn We Visulize the E Field? Vecto Mps: ow length indictes vecto mgnitude O Gphs: E, E, E z s function of (,, z) E, E θ, E Φ s function of (, θ, Φ) chg E Emple Conside point chge fied t the oigin of co-odinte sstem s shown. The following gphs epesent the functionl dependence of the Electic Field. Q φ E E E 0 0 φ 2π As the distnce fom the chge inceses, the field flls off s 1/ 2. At fied, the dil component of the field is constnt, independent of φ!!

5 Lectue 1 5 Lectue 2, ACT 2 Conside point chge fied t the oigin of co-odinte sstem s shown. Which of the following gphs best epesents the functionl dependence of the Electic Field t the point (,φ)? Q φ E E E Fied >0 0 φ 2π 0 φ 2π 0 φ 2π Anothe W to Visulize E... The Old W: Vecto Mps A New W: Electic Field Lines O O O chg - chg Lines leve positive chges nd etun to negtive chges Numbe of lines leving/enteing chge = mount of chge Tngent of line = diection of E Densit of lines = mgnitude of E

6 Lectue 1 6 Electic Dipole Q Wht is the Electic Field geneted b this chge θ ngement? -Q E E Clculte fo pt long -is: (,0) E =?? E =?? Smmet Electic Dipole: Field Lines Lines leve positive chge nd etun to negtive chge Wht cn we obseve bout E? E (,0) = 0 E (0,) = 0 Field lgest in spce between the two chges We deived:... fo >>,

7 Lectue 1 7 Field Lines fom 2 Like Chges Note the field lines fom 2 like chges e quite diffeent fom the field lines of 2 opposite chges (the electic dipole) Thee is zeo hlfw between chges >>: looks like field of point chge (2q) t oigin. Lectue 2, ACT 3 Q 2 -Q Conside dipole ligned with the -is s shown. Which of the following sttements bout E (2,) is tue? q 1 q 2 () E (2,) < 0 (b) E (2,) = 0 (c) E (2,) > 0

8 Lectue 1 8 E Q -Q Electic Dipole Wht is the Electic Field geneted b this chge ngement? Now clculte fo pt long -is: (0,) E =?? E =?? Coulomb Foce Q 0, = 4πε Rdil E ( ) 0 Q E ( 0, ) = 4πε ( ) ( ) Electic Dipole Q Cse of specil inteest: (ntenns, molecules) > > -Q Fo pts long -is: Fo pts long -is: Fo >>, E (,0) 2 1 πε 4 0 Q 3 Fo >>, Q E ( 0, ) = 4πε E ( 0, ) 4 1 πε Q 3

9 Lectue 1 9 Q -Q Electic Dipole Summ Cse of specil inteest: (ntenns, molecules) > > Along -is Along -is E (,0) 2 1 πε 4 0 Q Along bit ngle Θ 3 E ( 0, ) 4 1 πε 4 0 Q 3 dipole moment with Electic Fields fom Continuous Chge Distibutions Pinciples (Coulomb's Lw Lw of Supeposition) emin the sme. Onl chnge: See Emples in tet Σ P ΔE Δq

10 Lectue 1 10 Chge Densities How do we epesent the chge Q on n etended object? totl chge Q smll pieces of chge dq Line of chge: λ = chge pe unit length Sufce of chge: σ = chge pe unit e Volume of chge: ρ = chge pe unit volume dq = λ d dq = σ da dq = ρ dv Emple: Infinite line of chge E() =?

11 Lectue 1 11 How do we ppoch this clcultion? In wods: dd up the electic field contibution fom ech bit of chge, using supeposition of the esults to get the finl field E() =? In pctice: Use Coulomb s Lw to find the E field pe segment of chge Pln to integte long the line : fom to OR θ: fom π/2 to π/2 Θ An smmeties? This m help fo es cncelltions. Infinite Line of Chge Chge densit = λ de Θ ' We need to dd up the E field contibutions fom ll segments d long the line. d

12 Lectue 1 12 Infinite Line of Chge We use Coulomb s Lw to find de: But wht is dq in tems of d? And wht is in tems of? Theefoe, de Θ ' d But nd θ e not independent! = tnθ d = sec 2 θ dθ Components: Infinite Line of Chge E θ de E θ ' Integte: E = de = π/ 2 1 πε π/ d λdθ sin θ E = de = π/ 2 1 πε π/ λdθ cosθ

13 Lectue 1 13 Solution: / 2 π sinθdθ = 0 π / 2 π /2 cosθdθ = 2 π / 2 Conclusion: Infinite Line of Chge de Θ ' d The Electic Field poduced b n infinite line of chge is: evewhee pependicul to the line is popotionl to the chge densit deceses s 1/. Lectue 2, ACT 4 Conside cicul ing with unifom chge distibution (λ chge pe unit length) () s shown. The totl chge of this ing is Q. The electic field t the oigin is zeo (b) (c) R

14 Lectue 1 14 Summ Electic Field Distibutions Dipole ~ 1 / R 3 Point Chge ~ 1 / R 2 Infinite Line of Chge ~ 1 / R Motion of Chged Pticles in Electic Fields Remembe ou definition of the Electic Field, And emembeing Phsics 1501, Now conside pticles moving in fields. Note tht fo chge moving in constnt field this is just like pticle moving ne the eth s sufce. = 0 = constnt v = v o v = v o t = o v o t = o v o t ½ t 2

15 15 Lectue 1 Motion of Chged Pticles in Electic Fields Conside the following set up, e Fo n electon beginning t est t the bottom plte, wht will be its speed when it cshes into the top plte? Spcing = 10 cm, E = 100 N/C, e = C, m = kg Motion of Chged Pticles in Electic Fields v o = 0, o = 0 v f 2 v o 2 = 2Δ O, e

16 16 Lectue 1 Recp of tod s lectue Define Electic Field in tems of foce on "test chge" Electic Field Lines Emple Clcultions Continuous chge distibutions => integte Moving chges: Use Newton s lw Homewok #1 on Msteing Phsics Fom Chpte 20