II. Electric Field. II. Electric Field. A. Faraday Lines of Force. B. Electric Field. C. Gauss Law. 1. Sir Isaac Newton ( ) A.

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II. Electic Field D. Bill Pezzaglia II. Electic Field. Faaday Lines of Foce B. Electic Field C. Gauss Law Updated 08Feb010.

Si Isaac Newton (164-177) Poposes gavity must act instantaneously, egadless of distance (else angula momentum not conseved).

..that one body may act upon anothe at a distance though a vacuum without the mediation of anything else, by and though which thei action and foce may be conveyed fom one to anothe, is to me so geat

1 II. Electic Field D. Bill Pezzaglia II. Electic Field. Faaday Lines of Foce B. Electic Field C. Gauss Law Updated 08Feb010. Lines of Foce 1) ction at a Distance ) Faaday s Lines of Foce ) Pinciple of Locality 1. Si Isaac Newton ( ) Poposes gavity must act instantaneously, egadless of distance (else angula momentum not conseved). actio in distans (action at a distance), no mechanism poposed to tansmit gavity "...that one body may act upon anothe at a distance though a vacuum without the mediation of anything else, by and though which thei action and foce may be conveyed fom one to anothe, is to me so geat an absudity that, I believe no man, who has in philosophic mattes a competent faculty of thinking, could eve fall into it." 4 Poblems with ction at a Distance How does moon know that the eath is thee pulling on it? 5 a. Si Humphy Davy How is gavity tansmitted? Why does it follow invese squae law? Does it violate causality if instantaneous? 1807 Electolysis, used to sepaate salts. Founds science of electochemisty. Coulomb s law has same issues Newton himself wites: "...that one body may act upon anothe at a distance though a vacuum without the mediation of anything else, by and though which thei action and foce may be conveyed fom one to anothe, is to me so geat an absudity that, I believe no man, who has in philosophic mattes a competent faculty of thinking, could eve fall into it." 1675 Newton poposes an ethe to tansmit foces between bodies His geatest discovey was Michael Faaday takes Faaday with him on gand tou visiting mpee and Volta. 1

filings ove a magnetic show field lines Electic chages ceate electic field lines

deteministic, ambiguity which way to go) Density of lines is popotional to the

a physical existence in that intemediate space.

exist as distotions in the aethe of space ltenative to action at a distance,

He can t put them into mathematical fom. B. Electic Field 11 1a.

2 b. Michael Faaday c. Electic Lines of Foce Fist poposes ideas of Lines of Foce Example: ion filings ove a magnetic show field lines Electic chages ceate electic field lines Field lines stat on + chages, end on plus chage will tend to move along these lines d. Othe Popeties 9. Pinciple of Locality 10 Field Lines can t coss (else physics would not be deteministic, ambiguity which way to go) Density of lines is popotional to the stength of the foce I cannot conceive cuved lines of foce without the conditions of a physical existence in that intemediate space. (Michael Faaday) gues that the field lines have independent eality Foce fields exist as distotions in the aethe of space ltenative to action at a distance, paticles Locally inteact with foce lines Ideas ejected by othes. He can t put them into mathematical fom. B. Electic Field 11 1a. James Maxwell ( ) 1 1) Definition of Field ) Souces of Field ) Electodynamics 1855 essay On Faaday's Lines of Foce, suggests lines ae like an imaginay incompessible fluid (obeying hydodynamic equations) 1861 pape On Physical Lines of Foce, poposes eal physical model of votices fo magnetic field

3 1b. Definition of Field Definition: foce pe unit test chage (i.e. don t want test chage to affect field) F E Lim q 0 q 1 1c. nalogy to Gavity F g Lim m 0 m Gavitational Foce Field: foce pe unit test mass i.e. its an acceleation of gavity field 14 Units of Newton/Coul (o Volts/mete) Mass is the chage of gavity: F mg. Souces of E Field 15.a Monopole Souces 16 (a)point Chage Souce (monopoles (b)dipoles (c) Field of Dipole (incomplete) positive chage is a souce of electic field. Field adiates outwad fom a point souce negative chage is a sink of electic field. Field adiates inwad Field stength: EkQ/.b Dipole Souces 17.c Field of Dipole 18 n electic dipole is a stick of length L with + chage on one end and equal chage on othe. Deivation will be done on boad. Basically you use supeposition of fields of two monopoles. Dipole moment: pql The vecto p points along axis fom to + chage Units(SI) is C m Standad in Chemisty is the Debye: 1D.564x10-0 C m Field of dipole along its axis dops off like the cube of the distance! E( z) kq 1 1 ( z L) ( z + L) kq k p z

4 . Electodynamics a) Point Chages 19 B..a Point Chage Electodynamics Foce on monopole test chage q is: F q E 0 b) Toques on Dipoles c) Gadient Foces Foce between dipole p and monopole q is hence: kpq F q E z n extenal electical field causes the chages to eaange which cancels the field inside. Faaday Cage (196) 1 B..b Toque on Dipole Toque is defined Toque on a dipole in an electic field is: (deivation in class) τ F τ p E B..c Gadient Foces on Dipole C. Gauss s Law 4 If field is not constant (has a gadient ) then thee will be a foce on a dipole ΔE F qe( x+ L/) qe( x L/) p Δx With calculus, foce between dipoles (along a line) can be shown to be: F 6k p p z 1 4 1) Electic Flux ) Gauss Law (181) ) pplications 4

1. Electic Flux 5 b. Definition: Electic Flux 6 (a) Review: Flux of fluid would be the total flow of density ρ though a suface aea, i.e. the flow ate in kg pe second.

(Watts), wheeas the Intensity has units of Watts/m.

Lambet s Law (1760) Intensity is educed by cosine of angle of incidence Flux is the dot poduct of the electic field vecto with the aea vecto (which is nomal to the suface) Ψ E E cosθ

that the Total flux ove a closed suface is zeo E d 0 8 b. Souce of Flux 9 c. Gauss s Law 0 The net flux out of a closed suface must be due to a souce inside.

5 1. Electic Flux 5 b. Definition: Electic Flux 6 (a) Review: Flux of fluid would be the total flow of density ρ though a suface aea, i.e. the flow ate in kg pe second. Electic flux is defined to be the electic field (aka electic intensity ) times the aea it flows though Δm ( ρ v) Δt Ψ E Fo light passing though a window, the flux is the total powe (Watts), wheeas the Intensity has units of Watts/m. Powe[Intensity] x ea Units: [Ψ]volt meten m /C (c) Lambet s Law Sunlight coming in at a low altitude angle will have its enegy spead out ove moe aea. Lambet s Law (1760) Intensity is educed by cosine of angle of incidence Flux is the dot poduct of the electic field vecto with the aea vecto (which is nomal to the suface) Ψ E E cosθ 44. Consevation of Flux (a) Review: If no souces o sinks of fluid, then flux influx out (continuity equation) ρ 1v1 1 ρv nothe way of saying this is that the flow lines ae continuous o that the Total flux ove a closed suface is zeo E d 0 8 b. Souce of Flux 9 c. Gauss s Law 0 The net flux out of a closed suface must be due to a souce inside. Conside a point chage at the cente, then the electic flux would be: ( 4π ) Q Q Ψ E 4πε 0 ε 0 Note that the esult is INDEPENDENT of adius. In geneal: The total electic flux though a closed suface is popotional to the TOTL enclosed chage Q Ψ E ε 0 This fom is eally only useful fo vey symmetic situations. The moe geneal equation involves vecto calculus which is beyond the scope of this couse: E ρ ε 0 5

6 . pplications of Gauss s Law 1 b. Cylindical Geomety (a) Spheical Geomety: If the chage distibution is unifomly spheical, then we have the familia invese squae law esult Ψ E Ψ Q 4π 4πε0 Conside a line of chage (such as chage on a wie). The diamete of the wie eally doesn t matte! Ou Gaussian Suface is a cylinde of adius The flux out the ends does not count because the electic field is paallel to those sufaces Note that this is valid even if the chage is spead out ove a ball (e.g. the suface of a metal sphee). It also tells us that the electic field INSIDE a hollow ball of chage must be zeo! Ψ Ψ Q / L E π L πε 0 c. Plane Geomety Conside a flat sheet (aea ) with chage Q spead out unifomly. Ou Gaussian Suface is box with top and bottom of aea The flux out the ends does not count because the electic field is paallel to those sufaces, hence the height of the box can be anything, which tells us the electic field is INDEPENDENT of the distance fom the sheet (constant field). Refeences Ψ E Q ε 0 (This esult fist noted by Laplace 181) 6

Module 05: Gauss s s Law a

Module 05: Gauss s s Law a 1 Gauss s Law The fist Maxwell Equation! And a vey useful computational technique to find the electic field E when the souce has enough symmety. 2 Gauss s Law The Idea The total