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Homework Statement
[tex]\int_{S}[/tex][tex]\int[/tex] n dS = 0 for any closed surface S.
Homework Equations
The Attempt at a Solution
I can't solve this because I don't have any idea in Vector intregrals.
Homework Statement
[tex]\int_{S}[/tex][tex]\int[/tex] n dS = 0 for any closed surface S.
Homework Equations
The Attempt at a Solution
I can't solve this because I don't have any idea in Vector intregrals.
Homework Statement
Homework Equations
The Attempt at a Solution
Hint: The result is a vector, so look at its components. The x component of a vector V is [itex] V \cdot i[/itex]. So look at, for example:
[tex] i \cdot \int\int_S \hat n\ dS = \int\int_S i\cdot \hat n\ dS[/tex]
i is the unit vector in the x direction, the usual i,j,k notation. n is the unit outward normal.
If the vector field is always tangential to the surface (and therefore perpendicular with the normal of the surface), this relation is trivially true. If the vector field is 0 everywhere, then this relation is also trivially true. What is the question exactly? Find all such vector fields n for which this relation holds?
If the vector field is always tangential to the surface (and therefore perpendicular with the normal of the surface), this relation is trivially true. If the vector field is 0 everywhere, then this relation is also trivially true. What is the question exactly? Find all such vector fields n for which this relation holds?
So, will you help me to make a proof?