chapter24_2

# chapter24_2 - Electric Flux and Gauss Law Electric flux,...

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Electric Flux and Gauss Law Electric flux, definition cos E i i i i i E Aθ ∆Φ = = E A r r 0 surface lim i E i i A E E A d Φ = Φ = E A r r Gauss law q in is the net charge inside the surface 0 A E ε Φ in E q d = = r r

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Applying Gauss Law To use Gauss law, you need to choose a gaussian surface over which the surface integral can be simplified and the electric field determined Take advantage of symmetry Remember, the gaussian surface is a surface you choose, it does not have to coincide with a real surface
Conditions for a Gaussian Surface Try to choose a surface that satisfies one or more of these conditions: The value of the electric field can be argued from symmetry to be constant over the surface The dot product of can be expressed as a simple algebraic product EdA because and are parallel . The dot product is 0 because and are perpendicular The field is zero over the portion of the surface E r d i E A r r E r d A r d A r Still no clue how to use Gauss Law? There are only three types of problems. See examples in the following pages.

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Problem type I: Field Due to a Spherically Symmetric Even Charge Distribution, including a point charge. The field must be different inside ( r <a ) and outside ( r > a ) of the sphere. For r > a, s elect a sphere as the gaussian surface, with radius r and Symmetric to the original sphere. Because of this symmetry, the electric field direction radially along r, and at a given r , the field magnitude is a constant. r E E r r r 2 2 2 0 0 2 4 1 4 A E A E r Q k r Q k r q E q r E d d e e in in E = = = = = = = πε ε π Φ E is constant at a given r . Gauss Law As if the charge is a point charge Q
Field inside the sphere For r < a, s elect a sphere as the gaussian surface. All the arguments are the same as for r > a. The only difference is here q in < Q Find out that q in = Q( r/a ) 3 (How?) r r r r r 3 3 3 a a a Q k r Q k Q r r k r q k r q E q r E d d e e e in e in in E = = = = = = = = = E 3 2 2 2 0 0 2 1 4 1 4 A E A E πε ε π Φ Increase linearly with r, not with 1/ r 2

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Plot the results (assume positive Q )
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## This note was uploaded on 05/06/2008 for the course PHYS 1304 taught by Professor Ye during the Spring '08 term at SMU.

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chapter24_2 - Electric Flux and Gauss Law Electric flux,...

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