6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Derivatives and Electrostatics Corinne Manogue Tevian Dray

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Presentation transcript:

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Derivatives and Electrostatics Corinne Manogue Tevian Dray

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Scalar Fields

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Scalar Fields in 3-D

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Vector Fields We use the idea of field lines for electric fields because: –They are a concrete representation of Gauss’s law—they only end on charges. It is difficult to see three dimensional vectors on a two dimensional graph.

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Concept of Flux

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Visualizing Flux Initially, define the location of the point charge to be at the origin of a rectangular coordinate system: > Point:=[0,0,0]; > a:=Point[1];b:=Point[2];c:=Point[3]; Find the electric field of the point charge: > r:=sqrt((x-a)^2+(y-b)^2+(z-c)^2); > Efield:=(q/(4*Pi*epsilon))*grad(-1/r,[x,y,z]);

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Flux Maple Worksheet

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Relating Multiple Representations

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Flux out of the Top and Bottom of a Cube

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Flux out of an Entire Cube The total flux out of the cube is equal to the divergence of the field times the volume of the cube.

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Visualizing Divergence

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Divergence Theorem Divide your volume into many small boxes. Use the definition of divergence on each one.

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Differential Form of Gauss’s Law

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Curvilinear Coordinates

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Curvilinear Basis Vectors

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Curvilinear Basis Vectors

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Vector Differential

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Vector Differential

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Geometry of Change

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Master Formula where

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA The Hill

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Visualization—Gradient

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Cross Product

6 October 2010XIII SEMANA DE LA ENSENANZA DE LA FISICA Cross Product