Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by?
$begingroup$
Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by $x^2+y^2=a^2, z=x+1, z=0$ and $n$ is the outward drawn unit normal and the vector function $vec{F}=langle2x,-3y,zrangle$
My question is, can I directly apply the divergence theorem in this?
Using the divergence theorem, since divergence of F is zero, we are getting zero.
vector-analysis vector-fields
asked Jan 10 at 12:51
AbhayAbhay
3739
$endgroup$
add a comment |
$begingroup$
Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by $x^2+y^2=a^2, z=x+1, z=0$ and $n$ is the outward drawn unit normal and the vector function $vec{F}=langle2x,-3y,zrangle$
My question is, can I directly apply the divergence theorem in this?
Using the divergence theorem, since divergence of F is zero, we are getting zero.
vector-analysis vector-fields
asked Jan 10 at 12:51
AbhayAbhay
3739
$endgroup$
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11
add a comment |
$begingroup$
Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by $x^2+y^2=a^2, z=x+1, z=0$ and $n$ is the outward drawn unit normal and the vector function $vec{F}=langle2x,-3y,zrangle$
My question is, can I directly apply the divergence theorem in this?
Using the divergence theorem, since divergence of F is zero, we are getting zero.
vector-analysis vector-fields
asked Jan 10 at 12:51
AbhayAbhay
3739
$endgroup$
Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by $x^2+y^2=a^2, z=x+1, z=0$ and $n$ is the outward drawn unit normal and the vector function $vec{F}=langle2x,-3y,zrangle$
My question is, can I directly apply the divergence theorem in this?
Using the divergence theorem, since divergence of F is zero, we are getting zero.
vector-analysis vector-fields
vector-analysis vector-fields
asked Jan 10 at 12:51
AbhayAbhay
3739
asked Jan 10 at 12:51
AbhayAbhay
3739
asked Jan 10 at 12:51
AbhayAbhay
3739
asked Jan 10 at 12:51
AbhayAbhay
3739
asked Jan 10 at 12:51
AbhayAbhay
3739
3739
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11
add a comment |
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
5,204718
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3068608%2fevaluate-int-vecf-nds-where-s-is-the-entire-surface-of-the-solid-formed%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
5,204718
$endgroup$
add a comment |
$begingroup$
You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
5,204718
$endgroup$
add a comment |
$begingroup$
You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
5,204718
$endgroup$
You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
5,204718
edited Jan 10 at 16:57
answered Jan 10 at 16:52
Shubham JohriShubham Johri
5,204718
answered Jan 10 at 16:52
Shubham JohriShubham Johri
5,204718
answered Jan 10 at 16:52
Shubham JohriShubham Johri
5,204718
5,204718
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3068608%2fevaluate-int-vecf-nds-where-s-is-the-entire-surface-of-the-solid-formed%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11