Vector field

  • #1
likephysics
636
2

Homework Statement



[tex]\int[/tex] delxA dv = -[tex]\oint[/tex] Axds

where A is a vector field
Left hand side is integral over volume. Right hand side is integral over closed surface.

Homework Equations





The Attempt at a Solution



Can't understand what Axds means.
 

Answers and Replies

  • #2
payumooli
48
0
A is the vector field
and dS is the closed surface on which you want to see the flux
x is a multiplication symbol
 
  • #3
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,568
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Presumably what you are calling ds (which is usually used for an element of arc length) should be the vector surface element. If the surface is parameterized as

[tex]\vec R = \vec R(u,v) = \langle x(u,v),y(u,v),z(u,v)\rangle[/tex]

the surface element is

[tex]d\vec S = \vec R_u \times \vec R_v\, dudv[/tex]
 

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