This preview shows pages 1–11. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECSE 351 Electromagnetic Fields McGill University ECE Dept.  Prof. Milica Popovi Lectures 5 & 6: Electric Flux Density, Gausss Law and Divergence Objective: for symmetrical charge distributions, use Gausss Law to easily calculate the Efield intensity vector. Divergence: important operator (acts on a vector, returns a scalar) in vector field analysis. Gausss law but in a slightly different form is one of the Maxwells equations. Faradays experiment with two conductive and mutually insulated spheres: inner sphere is charged with Q and causes exactly Q to appear on the outer sphere! McGill ECE ECSE 351 Electromagnetic Fields Prof. M. Popovic Michael Faraday (17911867) Oil painting by T. Phillips, 1842. In the National Portrait Gallery, London. Electric Flux is proportional to the Q that causes it Electric flux density vector, is, generally, a function of coordinates. It shows the flux distribution over a surface and has a nature of a vector field McGill ECE ECSE 351 Electromagnetic Fields Prof. M. Popovic For a single charge density, the action of Q through the flux of its field is given over spherical concentric surfaces around it. McGill ECE ECSE 351 Electromagnetic Fields Prof. M. Popovic Have you seen a similar formula before? Link: electric flux density & electric field intensity vectors McGill ECE ECSE 351 Electromagnetic Fields Prof. M. Popovic This proportionality is valid only in vacuum (free space)! We will see later how dielectric materials are incorporated to modify this equation in a concise way. If you have many charges with a known volume distribution (so a general case) simply apply the principle of superpostion. McGill ECE ECSE 351 Electromagnetic Fields Prof. M. Popovic This proportionality is valid only in vacuum (free space)! We will see later how dielectric materials are incorporated to modify this equation in a concise way. Before we get to Gausss Law, some conventions McGill ECE ECSE 351 Electromagnetic Fields Prof. M. Popovic At each point of the surface, we define a vector surface element The normal is directed from the surface outward McGill ECE ECSE 351 Electromagnetic Fields Prof. M. Popovic Gausss Law McGill ECE ECSE 351 Electromagnetic Fields Prof. M. Popovic Johann Friedrich Carl Gauss April 30, 1777 , Brunswick [Germany]  February 23, 1855 , Gttingen, Hanover Gauss, oil painting by C.A. Jensen (17921870). In the Archiv der GeorgAugustUniversitt, Gttingen, Germany. Used for: Proofs of some general properties of ESfield Evaluation of Evector in cases with high degrees of symmetry of distribution of charges The flux of the electric flux density vector through any closed surface in the electrostatic field equals the total charge enclosed by the surface. Gausss Law McGill ECE ECSE 351 Electromagnetic Fields Prof. M. Popovic McGill ECE ECSE 351 Electromagnetic Fields Prof....
View
Full
Document
 Winter '08
 Davis

Click to edit the document details