A SHORT PRESENTATION ONGAUSS’S LAW : A SHORT PRESENTATION ONGAUSS’S LAW
Carl Friedrich Gauss 1777-1855 : Carl Friedrich Gauss 1777-1855 Yes it’s the same guy that gave you the Gaussian distribution and … To give you some perspective he was born 50 years after Newton died (1642-1727). Predicted the time and place of the first asteroid CERES (Dec. 31, 1801). Had the unit of magnetic field named after him and of course had much to do with the development of mathematics Ceres t= 4.6 year , d=4.6 Au
Definition of Flux : Definition of Flux The amount of field, material or other physical entity passing through a surface.
Surface area can be represented as vector defined normal to the surface it is describing
Defined by the equation:
FLUX : FLUX
FLUX : FLUX
Electric Flux : Electric Flux The amount of electric field passing through a surface area
The units of electric flux are N-m2/C
The Gaussian Surface : The Gaussian Surface An imaginary closed surface created to enable the application of Gauss’s Law What is the total flux through each surface?
Solving problems with Gauss’s Law : Solving problems with Gauss’s Law Determining the Electric Field from Gauss’s Law - We will use Gauss’s Law to determine the electric field for problems for which the Electric Field can be shown to be constant in magnitude in direction for a particular Gaussian surface.
Consider three examples: (1) the long straight line of charge, (2) the infinite plane sheet of charge, and (3) a charged sphere.
Example - Long straight line of charge : Example - Long straight line of charge Looking at the diagram (b), we can determine that the problem has a cylindrical symmetry.
Therefore cylindrical coordinates are appropriate. There are three surfaces to consider. The upper and lower circular surfaces have normals parallel to the z axis which are perpendicular to the electric field, thus contribute zero to the flux. The integral to be evaluated is that of the cylinder of height l. The charge enclosed is ll.
Example - Long straight line of charge : Example - Long straight line of charge Since the field has radial symmetry, it is also constant at a fixed distance of r.
Applied Gauss’ Law to Determine E-field in Cases where have : Applied Gauss’ Law to Determine E-field in Cases where have Spherical symmetry
Cylindrical symmetry
Planar symmetry
Shell Theorems: Conductors : Shell Theorems: Conductors A shell of uniform charge attracts or repels a charge particle that is outside the shell as though all charge is concentrated at the center.
If a charged particle is located inside such a shell, there is no electrostatic force on the particle from the shell
Results of other geometries : Results of other geometries Uniformly charged dielectric (insulating) sphere Uniformly charged dielectric infinite plane sheet Can you derive these results?
The electric flux passing through a spherical surface surrounding a point charge : The electric flux passing through a spherical surface surrounding a point charge
Conclusions Gauss’ LAW : Conclusions Gauss’ LAW Only the charge enclosed within a volume defined by a closed surface contributes to the net electric flux through the surface.
That net flux through the surface is proportional to the charge enclosed within the volume.
Conclusions : Conclusions 3. Gaussian surface is an imaginary closed surface necessary to solve a problem using Gauss’s Law
4. Gauss’s Law can be used to determine the electric field of a charge distribution if there is a high degree of symmetry
Slide 17 : 5. Applying Gauss’s Law to the interior of an electrostatically charged conductor we conclude that the electric field within the conductor is zero
6. Any Net charge on a conductor must reside on its surface Conclusion: Gauss’ Law and Conductors