New version page

UF PHY 2049 - Gauss’ Law

Documents in this Course
Subjects

Subjects

25 pages

Images

Images

6 pages

Magnetism

Magnetism

37 pages

Example

Example

10 pages

Optics

Optics

30 pages

Circuits

Circuits

47 pages

PLAN

PLAN

3 pages

Subjects

Subjects

15 pages

Circuits

Circuits

30 pages

OUTLINE

OUTLINE

6 pages

Circuits

Circuits

22 pages

Light

Light

7 pages

Circuits

Circuits

15 pages

Images

Images

26 pages

PLAN

PLAN

6 pages

Lecture 6

Lecture 6

21 pages

Load more
Upgrade to remove ads

This preview shows page 1-2-3-4-5 out of 14 pages.

Save
View Full Document
Premium Document
Do you want full access? Go Premium and unlock all 14 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 14 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 14 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 14 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 14 pages.
Access to all documents
Download any document
Ad free experience

Upgrade to remove ads
Unformatted text preview:

PHY2049: Chapter 231Chapter 23: Gauss’ LawPHY2049: Chapter 232Electric FluxÎSimple definition of electric flux (E constant, flat surface) E at an angle θ to planar surface, area A Units = N m2/ C (SI units)ÎSimple example Let E = 104N/C pass through 2m x 5m rectangle, 30° to normal φE= 104* 10 * cos(30) = 100,000 * 0.866 = 86,600ÎMore general ΦEdefinition (E variable, curved surface)cosEEAθΦ≡⋅ =EAESdΦ≡ ⋅∫EANormalEPHY2049: Chapter 233Example of Constant Field()2ˆˆ23mAij=+ˆ4Ei=()ˆˆˆ2348EijiΦ≡⋅ = + ⋅ =EAPHY2049: Chapter 234Flux Through Closed SurfaceÎSurface elements dAalways point outward!ÎSign of ΦEE outward (+) E inward (−)ΦE< 0ΦE= 0ΦE> 0PHY2049: Chapter 235Example: Flux Through CubeÎE field is constant: Flux through front face? Flux through back face? Flux through top face? Flux through whole cube?ˆEEz=GPHY2049: Chapter 236Example: Flux Through CylinderÎAssume E is constant, to the right Flux through left face? Flux through right face? Flux through curved side Total flux through cylinder?PHY2049: Chapter 237Example: Flux Through SphereÎAssume point charge +QÎE points radially outward (normal to surface!)()22044ESdkQrrQkQππεΦ= ⋅⎛⎞=⎜⎟⎝⎠==∫EAForeshadowing of Gauss’ Law!PHY2049: Chapter 238Gauss’ LawÎGeneral statement of Gauss’ lawÎCan be used to calculate E fields. But remember Outward E field, flux > 0 Inward E field, flux < 0ÎConsequences of Gauss’ law (as we shall see) E = 0 inside conductor E is always normal to surface on conductor Excess charge on conductor is always on surfaceConductorenc0Sqdε⋅=∫EAvIntegration over closedsurfaceqencis charge insidethe surfaceCharges outside surface have no effectPHY2049: Chapter 239Reading QuizÎWhat is the electric flux through a sphere of radius R surrounding a charge +Q at the center? 1) 0 2) +Q/ε0 3) −Q/ε0 4) +Q 5) None of thesePHY2049: Chapter 2310QuestionHow does the flux ФEthrough the entire surface change when the charge +Q is moved from position 1 to position 2?a) ФE increasesb) ФE decreasesc) ФE doesn’t changedSdS12+Q+QJust depends on chargenot positionPHY2049: Chapter 2311Power of Gauss’ Law: Calculating E FieldsÎValuable for cases with high symmetry E = constant, ⊥ surface E || surfaceÎSpherical symmetry E field vs r for point charge E field vs r inside uniformly charged sphere Charges on concentric spherical conducting shellsÎCylindrical symmetry E field vs r for line charge E field vs r inside uniformly charged cylinderÎRectangular symmetry E field for charged plane E field between conductors, e.g. capacitorsSdEA⋅=∫EAv0Sd⋅=∫EAvPHY2049: Chapter 2312ExampleÎ4 Gaussian surfaces: 2 cubes and 2 spheresÎRank magnitudes of E field on surfacesÎWhich ones have variable E fields?ÎWhat are the fluxes over each of the Gaussian surfaces(a) E falls as radius increases(b) E non-constant on cube (r changes)(c) Fluxes are same, +Q/ε0PHY2049: Chapter 2313Derive Coulomb’s Law From Gauss’ LawÎCharge +Q at a point By symmetry, E must be radially symmetricÎDraw Gaussian’ surface around point Sphere of radius r E field has constant mag., ⊥ to Gaussian surfaceGaussian surface(sphere)r()204SQdErπε⋅= =∫EAv2204QkQErrπε==Gauss’ LawSolve for EPHY2049: Chapter 2314ExampleÎCharges on shells are +Q (ball at center) +3Q (middle shell) +5Q (outside shell)ÎFind fluxes on the three Gaussian surfaces(a) Inner +Q/ε0(b) Middle +4Q/ε0(c) Outer


View Full Document
Download Gauss’ Law
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Gauss’ Law and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Gauss’ Law 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?