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# notes9 2317 - Flux Density ECE 2317 Applied Electricity and...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 9 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Notes prepared by the EM group, University of Houston . (used by Dr. Jackson, spring 2006) Flux Density Flux Density q E 2 0 0 2 2 4 [C/m ] 4 q Er r DE q Dr r πε ε π = = ± ± Define: “flux density vector” Flux Through Surface Flux Through Surface q D ± n S ± [] S D ndS C ψ ≡⋅ Example Example ± 2 2 4 4 S S S S Dnd S Drd S q rr d S r q dS r =⋅ ⎛⎞ ⎜⎟ ⎝⎠ = ± ±± v v v v (We want the flux going out) ± nr = ± x y z q D S Find the flux from a point charge going out through a spherical surface.

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Spherical Surface (cont.) Spherical Surface (cont.) () ( ) 2 2 2 00 2 0 sin 4 sin 4 2s i n 4 22 4 q rd d r q dd q d q ππ π ψ θθφ πθ θ ⎛⎞ = ⎜⎟ ⎝⎠ = = = ∫∫ [C] q = Flux Plot (3D) Flux Plot (3D) Rules: 1) Flux lines are in direction of D 2) #fluxlines area D S N D S Δ N S = # flux lines through Δ S S D S = small area perpendicular to the flux vector Flux Plot (2D)
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## This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Fall '08 term at University of Houston.

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notes9 2317 - Flux Density ECE 2317 Applied Electricity and...

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