What device provides a practical way to produce a uniform electric field?

Transcription

1 Chapte 7. The lectic Field lectic fields ae esponsible fo the electic cuents that flow though ou compute and the neves in ou bod. lectic fields also line up polme molecules to fom the images in a liquid cstal displa (LCD. Chapte Goal: To lean how to calculate and use the electic field. Chapte 7. The lectic Field Topics: lectic Field Models The lectic Field of Multiple Point Chages The lectic Field of a Continuous Chage Distibution The lectic Fields of ings, Disks, Planes, and Sphees The Paallel-Plate Capacito Motion of a Chaged Paticle in an lectic Field Motion of a Dipole in an lectic Field Chapte 7. eading uies What device povides a pactical wa to poduce a unifom electic field? A. A long thin esisto B. A Faada cage C. A paallel plate capacito D. A tooidal inducto. An electic field unifomie

2 What device povides a pactical wa to poduce a unifom electic field? A. A long thin esisto B. A Faada cage C. A paallel plate capacito D. A tooidal inducto. An electic field unifomie Fo chaged paticles, what is the quantit q/m called? A. Linea chage densit B. Chage-to-mass atio C. Chaged mass densit D. Massive electic dipole. uadupole moment Fo chaged paticles, what is the quantit q/m called? A. Linea chage densit B. Chage-to-mass atio C. Chaged mass densit D. Massive electic dipole. uadupole moment Which of these chage distibutions did not have its electic field detemined in Chapte 7? A. A line of chage B. A paallel-plate capacito C. A ing of chage D. A plane of chage. The wee all detemined

3 Which of these chage distibutions did not have its electic field detemined in Chapte 7? A. A line of chage B. A paallel-plate capacito C. A ing of chage D. A plane of chage. The wee all detemined The woked eamples of chagedpaticle motion ae elevant to A. a tansisto. B. a cathode a tube. C. magnetic esonance imaging. D. cosmic as.. lases. The woked eamples of chagedpaticle motion ae elevant to A. a tansisto. B. a cathode a tube. C. magnetic esonance imaging. D. cosmic as.. lases. Chapte 7. Basic Content and amples

4 lectic Field Models The electic field of a point chage q at the oigin,, is lectic Field Models The net electic field due to a goup of point chages is whee є 8.85 C /N m is the pemittivit constant. whee i is the field fom point chage i. Poblem-Solving Stateg: The electic field of multiple point chages Poblem-Solving Stateg: The electic field of multiple point chages

5 Poblem-Solving Stateg: The electic field of multiple point chages lectic Dipole: Two qual but Opposite Chages Sepaated b a Small Distance The lectic Field of a Dipole We can epesent an electic dipole b two opposite chages ±q sepaated b the small distance s. The dipole moment is defined as the vecto The dipole-moment magnitude p qs detemines the electic field stength. The SI units of the dipole moment ae C m. ( dipole The lectic Field of a Dipole On the ais of an electic dipole ( + ( q ( s ( q + ( + s / + / ( q s (.5 s ( +.5 s dipole >>s ( dipole qs 3

6 The lectic Field of a Dipole The electic field at a point on the ais of a dipole is whee is the distance measued fom the cente of the dipole. The electic field in the plane that bisects and is pependicula to the dipole is This field is opposite to the dipole diection, and it is onl half the stength of the on-ais field at the same distance. XAMPL 7. The electic field of a wate molecule USTION: XAMPL 7. The electic field of a wate molecule

7 XAMPL 7. The electic field of a wate molecule Tactics: Dawing and using electic field lines Tactics: Dawing and using electic field lines Continuous Chage Distibution: Chage Densit The total electic chage is. Volume V Linea, length L Amount of chage in a small volume dl: dq dl λ dl L λ L Linea chage densit Amount of chage in a small volume dv: ρ dq dv ρ dv V V Volume chage densit Suface, aea A Amount of chage in a small volume da: dq da σ da A σ A Suface chage densit

8 lectic Field: Continuous Chage Distibution Pocedue: Divide the chage distibution into small elements, each of which contains q Calculate the electic field due to one of these elements at point P valuate the total field b summing the contibutions of all the chage elements Smmet: take advantage of an smmet to simplif calculations lectic field due to thee equal point chages? Because the chage distibution is continuous q dq k lim ˆ k ˆ i e i e q i i i Fo the individual chage elements q k e ˆ lectic Field: Smmet q k ˆ e q µc q µc 5m, lectic field + 5m cosφ,, The lectic Field of a Continuous Chage Distibution at a point in the plane that bisects the ode + + 6m, + + φ cos, 4 4 cosφ, + + The smmet gives us the diection of esultant electic field

9 The lectic Field of a Continuous Chage Distibution ( i ( i cosθi i cosθ i The lectic Field of a Continuous Chage Distibution on a Thin od ( i ( i cosθi i ( i 4 πε + i cosθ i ( i 3/ 4 πε ( i + / L ( + + 3/ i i / L i L / λ ( / L d 3/ L / ( + How to evaluate this integal? -Tigonometic Substitution / L L / d 3 / L / ( + lectic Field due to a Thin od / L L/ d 3/ L/ ( + Use: (to evaluate, a tanθ, da sec θ dθ sinθ /( +a / / L 4 πε ( / + L / L L/ + L/ L/ L/ + ( L/ ( L/ +

10 πε An infinite Line of Chage 4 ( L / + line line line lim L ( L / 4 πε L / + negligible λ An infinite Line of Chage λ line Unlike a point chage, fo which the field deceases as /, the field of an infinitel long chaged wie deceases moe slowl as onl / Paallel-Plate Capacito Paallel-Plate Capacito Find electic field + + σ > σ ε σ > σ < σ < σ ε Find electic field σ σ + ε ε σ > σ < σ > σ < + σ + + ε +

11 Paallel-Plate Capacito σ > XAMPL 7.7 The electic field inside a capacito σ < USTIONS: σ ε σ > σ < XAMPL 7.7 The electic field inside a capacito XAMPL 7.7 The electic field inside a capacito

12 XAMPL 7.7 The electic field inside a capacito lectic Field: Continuous Chage Distibution on a ing What is the electic field at point P? P h o 9 O λ - linea chage densit What is the electic field at point P? λ - linea chage densit. Smmet detemines the diection of the electic field. o 9 O P h What is the electic field at point P? λ - linea chage densit. Divide the chage distibution into small elements, each of which contains q h o 9 O P all elements all elements all elements q cos ke cos q q k cos e q λ l l all elements

13 What is the electic field at point P? λ - linea chage densit What is the electic field at point P? λ - linea chage densit 3. valuate the total field b summing the contibutions of all the chage elements q h o 9 O P ψ l ψ q k cos e all elements l ψ q λ l λ ψ λ ψ ke cos all elements eplace Sum b Integal π λ d ψ ke cos 4. valuate the integal π π π π λ λ λ d ψ ke cos k cos cos e d ψ π k e h + h o 9 O P ψ h h cos h + l ψ k πλ e h ( h + 3/ 4 πε h 3/ ( h + A Cicula Disk of Chage lectic field due to a ing: η ( 4 πε h 3 / ( h + πε ( i i i 3 / A π 4 ( + i N N i ( disk 3/ i i ( + i N η i ( disk 3/ ε i ( + i η d ( disk 3/ ε ( + η ( disk ε + Motion of a Chaged Paticle ui: If >>, then?

14 Motion of Chaged Paticle Motion of Chaged Paticle When a chaged paticle is placed in an electic field, it epeiences an electical foce If this is the onl foce on the paticle, it must be the net foce The net foce will cause the paticle to acceleate accoding to Newton s second law F q - Coulomb s law What is the final velocit? F q - Coulomb s law F ma - Newton s second law a q m v f F ma q a m - Newton s second law Motion in with constant velocit Motion in with constant acceleation l t - tavel time v Afte time t the velocit in diection becomes v a q m v v q v a t t m then q v Copight 8 Peason ducation, Inc., publishing f v as Peason + t Addison-Wesle. m v v f Geneal Pinciples Chapte 7. Summa Slides

15 Geneal Pinciples Applications Applications Chapte 7. uestions

16 At the position of the dot, the electic field points A. Up. B. Down. C. Left. D. ight.. The electic field is eo. At the position of the dot, the electic field points A. Up. B. Down. C. Left. D. ight.. The electic field is eo. A piece of plastic is unifoml chaged with suface chage densit. The plastic is then boken into a lage piece with suface chage densit and a small piece with suface chage densit 3. ank in ode, fom lagest to smallest, the suface chage densities to 3. A. η η 3 >η B. η >η >η 3 C. η >η η 3 D. η 3 >η >η. η η η 3 A piece of plastic is unifoml chaged with suface chage densit. The plastic is then boken into a lage piece with suface chage densit and a small piece with suface chage densit 3. ank in ode, fom lagest to smallest, the suface chage densities to 3. A. η η 3 >η B. η >η >η 3 C. η >η η 3 D. η 3 >η >η. η η η 3

17 Which of the following actions will incease the electic field stength at the position of the dot? Which of the following actions will incease the electic field stength at the position of the dot? A. Make the od longe without changing the chage. B. Make the od fatte without changing the chage. C. Make the od shote without changing the chage. D. emove chage fom the od.. Make the od naowe without changing the chage. A. Make the od longe without changing the chage. B. Make the od fatte without changing the chage. C. Make the od shote without changing the chage. D. emove chage fom the od.. Make the od naowe without changing the chage. ank in ode, fom lagest to smallest, the electic field stengths a to e at these five points nea a plane of chage. A. a > c > b > e > d B. a b c d e C. a > b c > d e D. b c d e > a. e > d > c > b > a ank in ode, fom lagest to smallest, the electic field stengths a to e at these five points nea a plane of chage. A. a > c > b > e > d B. a b c d e C. a > b c > d e D. b c d e > a. e > d > c > b > a

18 ank in ode, fom lagest to smallest, the foces F a to F e a poton would epeience if placed at points a e in this paallel-plate capacito. A. F a F b F d F e > F c B. F a F b > F c > F d F e C. F a F b F c F d F e D. F e F d > F c > F a F b. F e > F d > F c > F b > F a ank in ode, fom lagest to smallest, the foces F a to F e a poton would epeience if placed at points a e in this paallel-plate capacito. A. F a F b F d F e > F c B. F a F b > F c > F d F e C. F a F b F c F d F e D. F e F d > F c > F a F b. F e > F d > F c > F b > F a Which electic field is esponsible fo the tajecto of the poton? Which electic field is esponsible fo the tajecto of the poton?