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LECTURE 6 slide 1

Lecture 6

Divergence, Gauss Law in

Differential Form

Sections: 3.4, 3.5, 3.6, 3.7

Homework: D3.6, D3.7, D3.8, D3.9; 3.15, 3.17, 3.19, 3.21,

3.25, 3.27

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LECTURE 6 slide 2

flux is the net normal flow of the vector field F through a surface

Flux 1

flux is positive when flow is outward and negative when flow is

inward

cosS S

d F ds = = F s

total flux implies integration over a closed surface

cosS S

d F ds = = F sw w

F is called the density of the flux

cos F n = a a

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LECTURE 6 slide 3

Flux 2

flux lines show the direction and density of the flux

ds

n

a

F

high density

low density

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LECTURE 6 slide 4

Flux Examples

0 ? =

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LECTURE 6 slide 5

Total Flux

Flux through a closed surface is a measure of the fields

sources in the enclosed volume.

S

d = F sw

0 =

source(positive flux) sink

(negative flux)no source(zero net flux)

0 > 0