Ene 325 electromagnetic fields and waves
This presentation is the property of its rightful owner.
Sponsored Links
1 / 20

ENE 325 Electromagnetic Fields and Waves PowerPoint PPT Presentation


  • 63 Views
  • Uploaded on
  • Presentation posted in: General

ENE 325 Electromagnetic Fields and Waves. Lecture 3 Gauss’s law and applications, Divergence, and Point Form of Gauss’s law. Review (1). Coulomb’s law Coulomb’s forc e electric field intensity or V/m.

Download Presentation

ENE 325 Electromagnetic Fields and Waves

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


Ene 325 electromagnetic fields and waves

ENE 325Electromagnetic Fields and Waves

Lecture 3 Gauss’s law and applications, Divergence, and Point Form of Gauss’s law


Review 1

Review (1)

  • Coulomb’s law

    • Coulomb’s force

    • electric field intensity

      or

      V/m


Ene 325 electromagnetic fields and waves

Review (2)

  • Electric field intensity in different charge configurations

    • infinite line charge

    • ring charge

    • surface charge


Outline

Outline

  • Gauss’s law and applications

  • Divergence and point form of Gauss’s law


Gauss s law and applications

Gauss’s law and applications

  • “The net electric flux through any closed surface is equal to the total charge enclosed by that surface”.

  • If we completely enclose a charge, then the net flux passing through the enclosing surface must be equal to the charge enclosed, Qenc.


Gauss s law and applications1

Gauss’s law and applications

  • The integral form of Gauss’s law:

  • Gauss’s law is useful in finding the fields for problems that have a high degree of symmetry by following these steps:

    • Determine what variables influence and what components of are present.

    • Select an enclosing surface, Gaussian surface, whose surface vector is directed outward from the enclosed volume and is everywhere either tangential to or normal to


Gauss s law and applications2

Gauss’s law and applications

  • The enclosing surface must be selected in order for to be constant and to be able to pull it out of the integral.


Ex1 determine from a charge q located at the origin by using gauss s law

Ex1 Determine from a charge Q located at the origin by using Gauss’s law.

1.

2. Select a Gaussian surface

3.Drat a fixed distance is constant and normal to a Gaussian surface, can be pulled out from the integral.


Ex2 find at any point p z from an infinite length line of charge density l on the z axis

Ex2 Find at any point P (, , z) from an infinite length line of charge density L on the z-axis.

1. From symmetry,

2. Select a Gaussian surface with radius  and length h.

3. D at a fixed distance is constant and normal to a Gaussian surface, can be pulled out from the integral. ant and normal to a Gaussian surface, can be pulled out from the integral.


Ene 325 electromagnetic fields and waves

Ex3 A parallel plate capacitor has surface charge +S located underneath a top plate and surface charge -S located on a bottom plate. Use Gauss’s law to find and between plates.


Ex4 determine electric flux density for a coaxial cable

Ex4 Determine electric flux density for a coaxial cable.


Ene 325 electromagnetic fields and waves

Ex5 A point charge of 0.25 C is located at r = 0 and uniform surface charge densities are located as follows: 2 mC/m2 at r = 1 cm and -0.6 mC/m2 at r = 1.8 cm. Calculate at

  • r = 0.5 cm

  • r = 1.5 cm


Ene 325 electromagnetic fields and waves

c) r = 2.5 cm


Divergence and point form of gauss s law 1

Divergence and Point form of Gauss’s law(1)

  • Divergence of a vector field at a particular point in space is a spatial derivative of the field indicating to what degree the field emanates from the point. Divergence is a scalar quantity that implies whether the point source contains a source or a sink of field.

where = volume differential element


Divergence and point form of gauss s law 2

Divergence and Point form of Gauss’s law(2)

or we can write in derivative form as

Del operator:

It is apparent that

therefore we can write a differential or a point form of Gauss’s law as


Divergence and point form of gauss s law 3

Divergence and Point form of Gauss’s law(3)

For a cylindrical coordinate:

For a spherical coordinate:


Physical example

Physical example

The plunger moves up and

down indicating net movement

of molecules out and in,

respectively.

  • positive indicates a source of flux. (positive charge)

  • negative indicates a sink of flux. (negative charge)

An integral form of Gauss’s law can also be written as


Ex 6 let determine

Ex6Let . Determine


Ene 325 electromagnetic fields and waves

Ex7Let C/m2 for a radius r = 0 to r = 3 m in a cylindrical coordinate system and for r > 3 m. Determine a charge density at each location.


Ene 325 electromagnetic fields and waves

Ex8 Let in a cylindrical coordinate system. Determine both terms of the divergence theorem for a volume enclosed by r = 1 m, r = 2 m, z = 0 m, and z = 10 m.


  • Login