- #1

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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.

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- Thread starter yusukered07
- Start date

- #1

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[tex]\int_{S}[/tex][tex]\int[/tex]

I can't solve this because I don't have any idea in Vector intregrals.

- #2

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- #3

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## Homework Statement

[tex]\int_{S}[/tex][tex]\int[/tex]ndS =0for 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

[tex] i \cdot \int\int_S \hat n\ dS = \int\int_S i\cdot \hat n\ dS[/tex]

- #4

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Hint: The result is a vector, so look at its components. The x component of a vectorVis [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]

What is i there???

n is normal line, I think

- #5

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- 767

- #6

Matterwave

Science Advisor

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- #7

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iis the unit vector in the x direction, the usuali,j,knotation.nis the unit outward normal.

So, will you help me to make a proof?

- #8

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is there any proof you can show??

that's the question..

- #9

gabbagabbahey

Homework Helper

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As LCKurtz already pointed out, [itex]\textbf{n}[/itex] is the outward unit normal to whichever closed surface is integrated over. The problem is to show that this integral is zero for any closed surface.

- #10

gabbagabbahey

Homework Helper

Gold Member

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So, will you help me to make a proof?

We don't make proofs for you here. LCKurtz has given you a very good hint in his first reply, try using it and show us what you get. You should find that the divergence theorem is very useful to you here

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