Transcription of Gauss’ Law
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Gauss’ Law
Fall 2008 Physics 231 Lecture 2-1 Gauss LawFall 2008 Physics 231 Lecture 2-2 Electric Field LinesThe number of field lines, also known as lines of force, are related to strength of the electric fieldMore appropriately it is the number of field lines crossing through a given surface that is related to the electric fieldFall 2008 Physics 231 Lecture 2-3 FluxHow much of something passes through some surfaceNumber of particles passing through a given surfaceTwo ways to defineNumber per unit area ( , 10 particles/cm2)Number passing through an area of interestFall 2008 Physics 231 Lecture 2-4 Electric FluxThe electric flux is defined to beAEE= Where E is the electric field and A is the areaFall 2008 Physics 231 Lecture 2-5 Electric FluxIf surface area is not perpendicular to the electric field we have to slightly change our definition of the flux cosAEE= Where is the angle between the field and the unit vector that is perpendicular to the surfaceFall 2008 Physics 231 Lecture 2-6 Electric FluxWe can see that the relationship betw
Electric Field is everywhere perpendicular to surface, i.e. parallel to surface normal Gauss’ Law then gives 3 0 3 3 0 2 0 4 4 R Q r E R Q r E r Q E dA encl πε ε π ε = = ∫ ⋅ = r r Field increases linearly within sphere Outside of sphere, electric field is given by that of a point charge of value Q
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