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# lecture5 - Gausss Law ctric Flux Ele Gausss Law ple Exam s...

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Gauss’s Law Electric Flux Gauss’s Law Examples

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Gauss’s Law Gauss’s Law What’s in thebox ??
Gauss’s Law Gauss’s Law What’s in thebox ?? Net # of lines going out is related to the Net chargeenclosed + + +

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Recall electric flux: dA uur E ur A E d E = - Scalar quantity - related to number of filed lines
For a closed surfaceS, theelement of area vectors point outward from the surface. Thesurfacemay be a real surface or just an ‘imaginary’ mathematical surfaceof our choosing. dA uur

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Gauss’s Law Gauss’s Law For a closed surfaceS, take the outward direction as thedirection for ; then… dA r Net outward flux through S net charge enclosed by S ο ε = 2 12 2 "permittivity of vacuum" 8.85 10 N C m ε ο - = × 1 and 4 e k ο ε π =
Or… The closed “Gaussian surface” S is arbitrary (and usually exists only in your imagination). o enclosed net S net Q A d E ε , = = Φ r r

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Example : point charge + r q E S: sphere, radius r, centered on the charge. dA E E Find themagnitudeof E on thesphere.
Solution:

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Example: Find the net outward flux for each surface + centered + outside + near edge
Example: +Q -2Q +3Q S S S S 1 , S 2 , and S

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