Lecture 9 Lecture Notes

Lecture 9 Lecture - outside sphere inside sphere Alternatively Tensor Notation Lecture Notes Page 2 inside sphere spherical coordinates with radius

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3.3.1 Derivation and definition of Maxwell Stress Tensor Maxwell Stress Tensor symmetric: define: electromechanic momentum density with surface normal Lec 09 - 21. Jan Thursday, January 22, 2009 9:45 PM Lecture Notes Page 1
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3.3.2 Force laws local representation of conservation law Poynting vector force density momentum density Integrated form: force on area G Force law now expressed exclusively in terms of fields: - external field - represents force per unit area acting on surface force on surface element (vector character!) 3.3.3: Example (Calculation details see Griffith, example 8.2, p. 353) Q: total charge R: radius of sphere uniformly charged sphere Total force acting on upper part of sphere ("northern hemisphere")?
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Unformatted text preview: outside sphere inside sphere Alternatively: Tensor Notation Lecture Notes Page 2 inside sphere spherical coordinates with radius coordinate r and radial unit vector surfaces: "bowl" "disc" = bowl + disc By symmetry: total force acts along z-direction with component bowl +disc Alternative way of calculation:-enlarge the area of integration by making the diameter D of bowl and D larger than the radius R of the sphere! ==> value of force on the larger volume is the same as over the old volume as the difference in volume does not contain any charges! ○ Integral over bowl goes to zero, as elements of Maxwell tensor scale as 1/D^4 ○ Integral over disc becomes integral over whole xy-Plane-take the limit of D to Infinity: Lecture Notes Page 3...
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This note was uploaded on 07/28/2009 for the course PHYS 441B taught by Professor Norbertlutkenhaus during the Winter '09 term at Waterloo.

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Lecture 9 Lecture - outside sphere inside sphere Alternatively Tensor Notation Lecture Notes Page 2 inside sphere spherical coordinates with radius

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