Phy 213 general physics iii
Download
1 / 11

Phy 213: General Physics III - PowerPoint PPT Presentation


  • 206 Views
  • Updated On :

Phy 213: General Physics III. Chapter 23: Gauss’ Law Lecture Notes. f. Electric Flux. Consider a electric field passing through a region in space. The electric flux , F E , is the scalar product of the average electric field vector and the normal area vector for the region, or:

Related searches for Phy 213: General Physics III

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Phy 213: General Physics III' - starbuck


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Phy 213 general physics iii l.jpg

Phy 213: General Physics III

Chapter 23: Gauss’ Law

Lecture Notes


Electric flux l.jpg

f

Electric Flux

  • Consider a electric field passing through a region in space. The electric flux , FE, is the scalar product of the average electric field vector and the normal area vector for the region, or:

  • Conceptually, the electric flux represents the flow of electric field lines (normal) through a region of space


Gauss law l.jpg
Gauss’ Law

  • Gauss’ Law is a fundamental law of nature relating electric charge to electric flux

  • According to Gauss’ Law, the total electric flux through any closed (“Gaussian”) surface is equal to the enclosed charge (Qenclosed) divided by the permittivity of free space (eo):

    or,

  • Gauss’ Law can be used to determine the electric field (E) for many physical orientations (distributions) of charge

  • Many consequences of Gauss’ Law provide insights that are not necessarily obvious when applying Coulomb’s Law


Gauss law for a point charge l.jpg
Gauss’ Law for a Point Charge

Consider a point charge, q

  • An appropriate “gaussian” surface for a point charge is a sphere, radius r, centered on the charge, since all E fields will be ∟ to the surface

  • The electric flux is:

  • Applying Gauss’ Law yields E:

q

r

Gaussian sphere


Spherical symmetry charged sphere l.jpg

Gaussian sphere

q

R

r

Spherical Symmetry: Charged Sphere

  • Spherical symmetry can be exploited for any spherical shape

  • Consider a hollow conducting sphere, radius R & charge q:

  • The flux through a “gaussian” sphere is:

  • Applying Gauss’ Law:

  • For r > R:

  • For r < R:

Inside a hollow conductor, E = 0


Spherical symmetry charged sphere 2 l.jpg

r

R

r

Gaussian sphere

Spherical Symmetry: Charged Sphere (2)

Consider a solid non-conducting sphere with radius R & uniform charge density, r:

  • Applying Gauss’ Law:

  • For r > R:

  • For r < R:

    Inside a uniformly charged insulator, E ≠ 0


Spherical symmetry charged spheres 3 l.jpg
Spherical Symmetry: Charged Spheres (3)

Consider 2 concentric hollow conducting spheres with radii R1 & R1 and charges q1 & q2:

  • Applying Gauss’ Law:

  • For r < R1:

  • For R2 > r > R1:

  • For r > R2: {opposite charge subtracts}

Gaussian sphere

q1

R1

r

R2

q2


Application line of charge l.jpg

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

l

0

r

x

Application: Line of Charge

  • Cylindrical symmetry is useful for evaluating a “line of charge” as well as charged cylindrical shapes

  • Consider an infinitely long line of charge, charge density l:

  • The flux through each of the 3 surfaces is:

  • Applying Gauss’ Law:


Planar symmetry a charged sheet l.jpg

Gaussian “pill-box” + + + + + + + +

Planar Symmetry: A Charged Sheet

  • A Gaussian “pill-box” is an appropriate Gaussian surface for evaluating a charged flat sheet

  • Consider a uniformly charged flat sheet with a surface charge density, s:

  • The flux through the pill-box surface is:

  • The electric field:


Application 2 parallel charged plates l.jpg

+q + + + + + + + +

Gaussian “pill-box”

-q

Application: 2 Parallel Charged Plates

  • Two oppositely charged conducting plates, with charge density s:

  • Surface charges draw toward each other on the inner face of each plate

  • To determine the electric field within the plates, apply a Gaussian “pill-box” to one of the plates

  • The flux through the pill-box surface is:

  • The electric field is:


Consequences of gauss law l.jpg
Consequences of Gauss’ Law + + + + + + + +

  • Electric flux is a conserved quantity for an enclosed electric charge

  • The electric field inside a charged solid conductor is zero

  • The electric field inside a charged hollow conductor or non-conductor is zero

  • Geometrical symmetries can make the calculation of an electric field less cumbersome even for complicated charge distributions