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

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Prof. David R. Jackson ECE Dept. Spring 2011 Notes 9 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism
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Flux Density Flux Density q E 2 0 0 2 2 ˆ 4 ˆ [C/m ] 4 q E r r D E q D r r πε ε π = = Define: “flux density vector”
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Flux Through Surface Flux Through Surface q D ˆ n S [ ] ˆ S D ndS C ψ≡ Define flux through a surface:
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Example Example 2 2 ˆ ˆ ˆ ˆ 4 4 S S S S D ndS D r dS q r r dS r q dS r ψ π = = = = Ñ Ñ Ñ Ñ (We want the flux going out.) ˆ ˆ n r = 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.) ( 29 ( 29 2 2 2 0 0 2 0 0 0 sin 4 sin 4 2 sin 4 2 2 4 q r d d r q d d q d q π π π ψ θ θ φ θ θ = = = = ∫ ∫ ∫ ∫ C [ ] q ψ=
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Flux Plot (3D) Flux Plot (3D) 1) Flux lines are in direction of D 2) # D fluxlines area S N D S N S = # flux lines through S S D S = small area perpendicular to the flux vector (The symbol means "proportional to".) Rules:
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Flux Plot (2D) Flux Plot (2D) 1) Lines are in direction of D 2) # D fluxlines length L N D L L
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notes9 2317 - ECE 2317 ECE Applied Electricity and...

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