Lec5&6-FluxGaussDiv

Lec5&6-FluxGaussDiv - ECSE 351 Electromagnetic...

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Unformatted text preview: ECSE 351 Electromagnetic Fields McGill University – ECE Dept. - Prof. Milica Popovi ć Lectures 5 & 6: Electric Flux Density, Gauss’s Law and Divergence Objective: for symmetrical charge distributions, use Gauss’s Law to easily calculate the E-field intensity vector. Divergence: important operator (acts on a vector, returns a scalar) in vector field analysis. Gauss’s law – but in a slightly different form – is one of the Maxwell’s equations. Faraday’s 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 (1791-1867) 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 Gauss’s 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 Gauss’s Law McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic Johann Friedrich Carl Gauss April 30, 1777 , Brunswick [Germany] - February 23, 1855 , Göttingen, Hanover Gauss, oil painting by C.A. Jensen (1792–1870). In the Archiv der Georg-August-Universität, Göttingen, Germany. Used for: Proofs of some general properties of ES-field Evaluation of E-vector 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. Gauss’s Law McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic McGill – ECE – ECSE 351 Electromagnetic Fields – Prof....
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Lec5&6-FluxGaussDiv - ECSE 351 Electromagnetic...

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