Flux through the surface of an ellipsoidCalculate the flux through a closed surfaceFlux Integral in spherical coordinatesFlux through a SurfaceEvaluating surface integral (1) directly and (2) by applying Divergence Theorem give different resolutsCompute the flux of the vector field $vecF$ through the surface SThe flux of the vector field $u = x hatimath + y hatjmath + z hatk$ through the surface of the ellipsoidFlux through surface (correct or not?)Calculation of flux through sphere when the vector field is not defined at the origincalculate flux through surfaceFlux of a hemisphere
How to find the largest number(s) in a list of elements, possibly non-unique?
Unfrosted light bulb
Which partition to make active?
Writing in a Christian voice
What is the tangent at a sharp point on a curve?
Symbolism of 18 Journeyers
Help with identifying unique aircraft over NE Pennsylvania
Exposing a company lying about themselves in a tightly knit industry: Is my career at risk on the long run?
Print a physical multiplication table
Homology of the fiber
Why I don't get the wanted width of tcbox?
Why is indicated airspeed rather than ground speed used during the takeoff roll?
Print last inputted byte
Do people actually use the word "kaputt" in conversation?
What are the consequences of changing the number of hours in a day?
Does the Shadow Magic sorcerer's Eyes of the Dark feature work on all Darkness spells or just his/her own?
Could any one tell what PN is this Chip? Thanks~
Why didn’t Eve recognize the little cockroach as a living organism?
How do researchers send unsolicited emails asking for feedback on their works?
What happens when the centripetal force is equal and opposite to the centrifugal force?
Is VPN a layer 3 concept?
Does convergence of polynomials imply that of its coefficients?
Isn't the word "experience" wrongly used in this context?
Why is participating in the European Parliamentary elections used as a threat?
Flux through the surface of an ellipsoid
Calculate the flux through a closed surfaceFlux Integral in spherical coordinatesFlux through a SurfaceEvaluating surface integral (1) directly and (2) by applying Divergence Theorem give different resolutsCompute the flux of the vector field $vecF$ through the surface SThe flux of the vector field $u = x hatimath + y hatjmath + z hatk$ through the surface of the ellipsoidFlux through surface (correct or not?)Calculation of flux through sphere when the vector field is not defined at the origincalculate flux through surfaceFlux of a hemisphere
$begingroup$
I was asked to calculate the flux of the field $$mathbf A = (1/R^2)hat r$$
where $R$ is the radius, through the surface of the ellipsoid $$left(fracx^2a^2right) + left(fracy^2b^2right) + z^2 = 1$$
Without doing the formal calculations (I have never encountered a problem like this), I neverless suspect that it's equivalent to the flux of the same field through the surface of a sphere whose radius is the mean radius of the ellipsoid (i.e. $4 pi$)...am I wrong and/or how to solve?
integration multivariable-calculus vector-analysis surface-integrals
asked Mar 13 at 10:43
Lo ScrondoLo Scrondo
19410
$endgroup$
add a comment |
$begingroup$
I was asked to calculate the flux of the field $$mathbf A = (1/R^2)hat r$$
where $R$ is the radius, through the surface of the ellipsoid $$left(fracx^2a^2right) + left(fracy^2b^2right) + z^2 = 1$$
Without doing the formal calculations (I have never encountered a problem like this), I neverless suspect that it's equivalent to the flux of the same field through the surface of a sphere whose radius is the mean radius of the ellipsoid (i.e. $4 pi$)...am I wrong and/or how to solve?
integration multivariable-calculus vector-analysis surface-integrals
asked Mar 13 at 10:43
Lo ScrondoLo Scrondo
19410
$endgroup$
add a comment |
$begingroup$
I was asked to calculate the flux of the field $$mathbf A = (1/R^2)hat r$$
where $R$ is the radius, through the surface of the ellipsoid $$left(fracx^2a^2right) + left(fracy^2b^2right) + z^2 = 1$$
Without doing the formal calculations (I have never encountered a problem like this), I neverless suspect that it's equivalent to the flux of the same field through the surface of a sphere whose radius is the mean radius of the ellipsoid (i.e. $4 pi$)...am I wrong and/or how to solve?
integration multivariable-calculus vector-analysis surface-integrals
asked Mar 13 at 10:43
Lo ScrondoLo Scrondo
19410
$endgroup$
I was asked to calculate the flux of the field $$mathbf A = (1/R^2)hat r$$
where $R$ is the radius, through the surface of the ellipsoid $$left(fracx^2a^2right) + left(fracy^2b^2right) + z^2 = 1$$
Without doing the formal calculations (I have never encountered a problem like this), I neverless suspect that it's equivalent to the flux of the same field through the surface of a sphere whose radius is the mean radius of the ellipsoid (i.e. $4 pi$)...am I wrong and/or how to solve?
integration multivariable-calculus vector-analysis surface-integrals
integration multivariable-calculus vector-analysis surface-integrals
asked Mar 13 at 10:43
Lo ScrondoLo Scrondo
19410
asked Mar 13 at 10:43
Lo ScrondoLo Scrondo
19410
asked Mar 13 at 10:43
Lo ScrondoLo Scrondo
19410
asked Mar 13 at 10:43
Lo ScrondoLo Scrondo
19410
asked Mar 13 at 10:43
Lo ScrondoLo Scrondo
19410
19410
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The field you are asked about is the prominent gravitational / Coulomb field which main characteristics is the fact that its divergence is $0$ everywhere except for the origin point $(0,0,0)$:
$$
nablacdotmathbf A=4pidelta(mathbf r),
$$
which is easy to check.
Therefore by divergence theorem the flux over the surface is $4pi$ since the origin point is inside the surface.
answered Mar 13 at 14:49
useruser
5,45411030
$endgroup$
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%2f3146401%2fflux-through-the-surface-of-an-ellipsoid%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
$begingroup$
The field you are asked about is the prominent gravitational / Coulomb field which main characteristics is the fact that its divergence is $0$ everywhere except for the origin point $(0,0,0)$:
$$
nablacdotmathbf A=4pidelta(mathbf r),
$$
which is easy to check.
Therefore by divergence theorem the flux over the surface is $4pi$ since the origin point is inside the surface.
answered Mar 13 at 14:49
useruser
5,45411030
$endgroup$
add a comment |
$begingroup$
The field you are asked about is the prominent gravitational / Coulomb field which main characteristics is the fact that its divergence is $0$ everywhere except for the origin point $(0,0,0)$:
$$
nablacdotmathbf A=4pidelta(mathbf r),
$$
which is easy to check.
Therefore by divergence theorem the flux over the surface is $4pi$ since the origin point is inside the surface.
answered Mar 13 at 14:49
useruser
5,45411030
$endgroup$
add a comment |
$begingroup$
The field you are asked about is the prominent gravitational / Coulomb field which main characteristics is the fact that its divergence is $0$ everywhere except for the origin point $(0,0,0)$:
$$
nablacdotmathbf A=4pidelta(mathbf r),
$$
which is easy to check.
Therefore by divergence theorem the flux over the surface is $4pi$ since the origin point is inside the surface.
answered Mar 13 at 14:49
useruser
5,45411030
$endgroup$
The field you are asked about is the prominent gravitational / Coulomb field which main characteristics is the fact that its divergence is $0$ everywhere except for the origin point $(0,0,0)$:
$$
nablacdotmathbf A=4pidelta(mathbf r),
$$
which is easy to check.
Therefore by divergence theorem the flux over the surface is $4pi$ since the origin point is inside the surface.
answered Mar 13 at 14:49
useruser
5,45411030
edited Mar 13 at 14:54
answered Mar 13 at 14:49
useruser
5,45411030
answered Mar 13 at 14:49
useruser
5,45411030
answered Mar 13 at 14:49
useruser
5,45411030
5,45411030
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%2f3146401%2fflux-through-the-surface-of-an-ellipsoid%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
