# aklec02 - 2 Static Fields and Potentials When sources have...

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2 Static Fields and Potentials When sources have no time variation, or when ) ( and ) ( r J J r The resulting fields have no time variation either, and they are functions of position r only: ) ( ), ( ), ( ), ( r H H r B B r D D r E E If we replace the time derivative by zero, static equations are obtained. 0 0 0 t 0 J H E B D D J H B E B D t t Assuming free-space, D = E and B = H are valid. Under static conditions, the fields (and equations) are decoupled. E and H can exist without the other.

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Electrostatics Electrostatic fields are observed when charges are at rest, or static with respect to the observer. Governing equations in free-space are: E D E D 0 0 Static E field is curl-free, i.e. there is no vector or rotating source for static E . As a result, it is conservative. Mathematically the line integral is path independent, or closed line integral of it is identically zero. Utilizing the vector identity static E can be expressed as where ) , , ( z y x V V is the electrostatic potential. So that a unique potential, (or potential difference wrt a reference) is assigned to every point in space. field scalar any for 0 ) ( C S d d 0 theorem Stokes' Apply 0 0 l E S E E V  E
Magnetostatics Static magnetic fields are observed when charges are moving with constant velocity with respect to the observer. Governing equations in free-space are: 0 0 H B J H B Utilizing the vector identity F F field any vector for 0 ) ( static B can be expressed as A B where ) , , ( z y x A A is the magnetic vector potential.

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Field Calculations The diagram below demonstrates the two possible approaches to field calculations. The simpler approach is chosen for the particular problem at hand. Usually potential approach is
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## This note was uploaded on 08/25/2011 for the course ECE 350 taught by Professor Kudeki during the Spring '11 term at University of Illinois at Urbana–Champaign.

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aklec02 - 2 Static Fields and Potentials When sources have...

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