Gauss law for cylinders
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1) The document discusses using Gauss' law to calculate the electric field inside and outside an infinitely long, uniformly charged cylinder. 2) It considers two cases: where the charge is distributed homogeneously throughout the cylinder or concentrated on the surface. 3) Gauss' law is applied using a cylindrical Gaussian surface to show that the electric field is radially directed and depends only on the distance from the cylinder's central axis.
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![Gauss’ Law for Cylinder Symmetry Question: Calculate E- field in arbitrary points inside and outside cilinder Two cases: A: homogeneously charged B: charged at surface walls only Available: Cilinder, radius R, infinitely long, carrying charge density [C/m]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Electric flux is the amount of electric field passing through a surface. It is calculated by taking the dot product of the electric field and a normal vector perpendicular to the surface, integrated over the surface area. Gauss's law equates the total electric flux passing through any closed surface to the net electric charge enclosed divided by the permittivity of free space. This relationship allows electric fields and fluxes to be calculated for symmetric charge distributions.
Gauss law
Gauss's law relates the electric flux through a closed surface to the electric charge enclosed by the surface. It states that the total electric flux Ψ through any closed surface is equal to 1/ε0 times the total charge Q enclosed by the surface. Gauss's law can be used to easily solve for electric fields and potentials of symmetric charge distributions such as point charges, line charges, and spherical charge distributions. It has applications in deriving Coulomb's law and calculating electric fields due to line charges, charged spheres, and infinite plane sheets of charge.
Lecture 3
Karl Gauss developed Gauss's law, which relates the electric flux through a closed surface to the electric charge enclosed by the surface. Gauss's law can be used to calculate electric fields produced by charge distributions or to determine charge distributions that produce known electric fields. When applying Gauss's law, it is important to choose a Gaussian surface where the electric field is constant, zero, or parallel to the surface area elements to simplify the flux calculations. Conductors in electrostatic equilibrium have no electric field inside their volume, any excess charge resides on the surface, and the electric field just outside is perpendicular to the surface with a magnitude proportional to the surface charge density.
ch10.5.pptx
This document section summarizes information about Euler paths and circuits as well as Hamilton paths and circuits. It discusses:
- Euler's solving of the Königsberg bridge problem and defining Euler paths/circuits
- Necessary and sufficient conditions for a graph to have an Euler path/circuit
- Algorithms for constructing Euler circuits
- Applications of Euler paths/circuits
- Defining Hamilton paths/circuits and discussing properties like Dirac's and Ore's theorems for Hamilton circuits
- Differences between Euler and Hamilton circuits
2 4 the_smith_chart_package
The Smith Chart provides a graphical tool for analyzing transmission lines and impedance matching circuits. It maps the reflection coefficient Γ onto a two-dimensional plane defined by the magnitude and phase of Γ. Transformations of Γ along a transmission line correspond to moving along a circular arc on the Smith Chart, allowing problems involving transmission line impedance transformations to be solved graphically. Special cases like quarter-wave and half-wave transmission lines correspond to rotations of 90 and 180 degrees on the Smith Chart.
PHYS_2326_012209 (1).pptxxxxxxxxxxxxxxxxx
The document discusses electric flux and Gauss's law. It defines flux as the rate of flow through an area and electric flux as the rate of flow of an electric field through an area. Gauss's law relates the electric flux through a closed surface to the net charge enclosed. It states that the flux is equal to the enclosed charge divided by the permittivity of free space. The document provides examples of calculating electric flux for different charge distributions and symmetries using Gauss's law.
ELECTRIC FLUX.pptxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Electric flux is the rate of flow of an electric field through a surface. Gauss's law relates the electric flux through a closed surface to the net electric charge enclosed by the surface. It states that the total flux is equal to 1/ε0 times the enclosed charge, where ε0 is the vacuum permittivity. Gauss's law is useful for calculating electric fields produced by symmetric charge distributions. It can be applied by choosing a Gaussian surface with the same symmetry as the charge arrangement and relating the flux through the surface to the enclosed charge.
Emfbook
This document provides information about ACE Educational Academy, an institution that provides training in electrical engineering. It includes a foreword about the book "Electromagnetic Fields" written by Venugopala Swamy for exams like GATE and engineering services. The book aims to explain electromagnetic field concepts simply. The document then lists topics that will be covered in the book, including vector analysis, electric fields, capacitance, Maxwell's equations, and inductance of simple geometries. It provides some introductory information about using vector analysis concepts like gradient, divergence and curl to solve electromagnetic field problems.
Lec 3-guass-law
The document discusses electric flux and Gauss's law. It begins by defining electric flux and showing how to calculate it through different oriented surfaces in an electric field. It then explains Gauss's law mathematically and how it can be used to calculate the electric field due to symmetric charge distributions like point charges, charged plates, and charged spherical shells by choosing a Gaussian surface and relating the flux to the enclosed charge. Recipes for setting up and solving Gauss's law problems are provided. Examples of applications like finding fields due to wires, plates, cylinders and spheres are also listed.
Similar to Gauss law for cylinders (20)
ELECTRIC FLUX.pptxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ELECTRIC FLUX.pptxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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- 1. Gauss’ Law for Cylinder Symmetry © Frits F.M. de Mul
- 2. Gauss’ Law for Cylinder Symmetry Question: Calculate E- field in arbitrary points inside and outside cilinder Two cases: A: homogeneously charged B: charged at surface walls only Available: Cilinder, radius R, infinitely long, carrying charge density [C/m]
- 4. Analysis and Symmetry (1) 2. Charge distribution: C/m] ; homogeneous. 4. Cylinder symmetry: 1. Cylinder : infinitely long, radius R 3. Coordinate axes: Z-axis = symm. axis Y X Z e z e r all points at equal r are equivalent, even if at different z or
- 5. Analysis and Symmetry (2) 5. Consequences : a point charge will not move tangentially. Y X Z 4. Cylinder symmetry: e z e r all points at equal r are equivalent, even if at different z or E directed radially everywhere. all planes z = const. are equivalent.
- 7. Calculations (1) top and bottom lids do not contribute ( E dA ) wall contributes: E. 2 rL charge enclosed: L result: E ( r ) = 2 r Gauss’ Law: Z E L pill box: radius r>R ; height L
- 8. Calculations (2) result: E ( r ) = 2 r but wait !! this holds for r>R ! A: homogeneously charged B: charged at surface only Gauss’ Law: Z L L for r<R :
- 9. Conclusions (1) field strength dependent of distance to cylinder => no homogeneous field A: homogeneously charged B: charged at surface only for infinite cylinder:
- 10. Conclusions (2) for infinite cylinder: A: homogeneously charged; B: surface charge only the end R 2 R r 0 E ( r ) A+B A B