Recent content by fibonacci101

Okay! This is my last try and I hope I will be right .. Given a closed Surface S, the vector Area of this is zero. so that is i.t.

So, How is it to be equal to zero? i don't know what to do. I thought I've already got the right solution. but it is quite wrong...

div F = \left[\frac{\partial}{x}\vector{i} + \frac{\partial}{y}\vector{j}+\frac{\partial}{z}\vector{k}\right]\left(\vector{ni} + \vector {nj} +\vector{nk}\right) = 0 right?

By the definition of divergence...see??

Is this for me?

Yeah.. That is 0... Thanks for helping and guiding me,Sir. Hope to guide me in my further studies.. Thanks again... I LOVE YOU! LOL

div F = \left[\frac{\partial}{x}\vector{i} + \frac{\partial}{y}\vector{j}+\frac{\partial}{z}\vector{k}\right]\left(\vector{i} + \vector {j} +\vector{k}\right) div F =\left[\frac{\partial}{x}\vector{0} + \frac{\partial}{y}\vector{0}+\frac{\partial}{z}\vector{0}\right] div F = 0 + 0 + 0...

Divergence Theorem said that \int\int_{S} \vec{F} \cdot \vec{n} dS = \int\int\int_{V} \nabla \cdot \vec{F} dV

how do you prove this? Prove that \int\int_{S} n dS = 0 for any closed surface [SIZE="3"]S.

\vec{n}=(\vec{i}\cdot\vec{n})\vec{i}+(\vec{j}\cdot \vec{n})\vec{j}+(\vec{k}\cdot\vec{n})\vec{k} Then, \int\int_{S}\vec{n}dS=\int\int_{S}(\vec{i}\cdot\vec{n})dS\vec{i}+\int\int_{S}(\vec{j}\cdot\vec{n})dS\vec{j}+\int\int _{S}(\vec{k}\cdot\vec{n})dS\vec{k} I stacked to this step...

I will conclude that \int\int_{S} F \cdot n dS = 0

Yeah, I get what you are saying... So If I choose an F a vector the solution will lead to Divergence Theorem? Am I right?

Is there a value of n(outward unit vector)?

my problem is how do I show that the \int\int_{S} n dS = 0 for any closed surface [SIZE="3"]S ----> I used the divergence theorem, but I don't think it will help me 'cause it is applicable for \int\int_{S} F{ \cdot} n dS not for \int\int_{S} n dS

Homework Statement Prove that \int\int_{S} n dS = 0 for any closed surface [SIZE="3"]S.Homework Equations The Attempt at a Solution I used divergence theorem. But i thought it is applicable only if there is another vector multiplied to that outward unit vector (n). \int\int_{S} F {\cdot} n dS