Tommynaut
  • Tommynaut
Let F = y^2 ~i + x ~j + z ~k. Let S be the curved surface of the cylinder x^2 + y^2 = 1 for 0 <= z <= 3. Calculate the outwards flux of F through S. I used the divergence theorem to get my solution, by finding divF = 1. I thought that would mean that the flux would be the volume of the cylinder, but the answer is actually 0. Could someone please explain the proper process? Oh, and is there a way to use latex when asking questions?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Empty
  • Empty
Yeah, like this for example and the code: $$\nabla \cdot F = 0 $$ ``` $$\nabla \cdot F = 0 $$ ```
Empty
  • Empty
Actually wait, you mean specifically while asking questions. No, it's not really possible to access the equation editor but you can still type latex, it sucks I agree. But whatever let me try help you with your actual problem, one sec haha.
Tommynaut
  • Tommynaut
Ok cheers haha

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Empty
  • Empty
Ahhh ok the problem I believe you're having is that the divergence theorem applies to closed shapes, not open ones.
Tommynaut
  • Tommynaut
But surely the cylinder can be imagined to be closed? I really didn't think it made a difference, especially as we're looking for the flux through the curved surface anyway.
Tommynaut
  • Tommynaut
And how would the question then be done?
anonymous
  • anonymous
You can only use the divergence theorem if the surface is closed.
anonymous
  • anonymous
I don't think the top and bottom are included.
anonymous
  • anonymous
It'd parametrize the cylinder as: \[ \{(\cos t, \sin t, z)|0\leq t\leq 2\pi,0\leq z\leq 3\} \]
dan815
  • dan815
you can apply div theorem, and them subtract the flux out of the top and bottom circles, if that simplfies it, it might be simplied to do the flux out of hte top and bottom as they are planar and perp to z so only the z component would matter
IrishBoy123
  • IrishBoy123
you should have gotten 3pi from div theorem surely. then the field on bottom plate = zero => zero flux normalised field at top plate = > z = 3, which is 3 pi also so net through curved surface = 0 which makes sense as the field is symmetrical in the x-y plane
Tommynaut
  • Tommynaut
I did indeed get 3pi originally. I don't really understand the concepts you guys are explaining but thank you anyway. I found a method of solution that uses cylindrical coordinates and the unit normal outwards, followed by a double integral.
IrishBoy123
  • IrishBoy123
i hope this helps
1 Attachment
IrishBoy123
  • IrishBoy123
my point being that, in my experience at least, doing these types of things is v often about not doing them. ie spotting symmetries in the set up, or lucking out with divergence or stoke's theorem, the alternative being to do a complete pig of a double integral....:p you can often also have more confidence in your answer if you have simplified it down in one of these ways.
Tommynaut
  • Tommynaut
Thank you for that! The notation you use is a bit different to what I've been taught but it makes sense nonetheless :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.