This thread is closed

Scroll to see replies

Bezza

That will only give you the flux through that 1 side of the tetrahedron that's bounded by the plane 2x + y + 2z = 4 whereas you need to sum the flux through all the sides.

If you put in x=y=0 then you see the plane crosses the z-axis at 2, then do similar things to get it crosses the x-axis at 2 and the y-axis at 4 then do a sketch.

I'm not too sure what he's done with that cross product either! He must be doing it to find a normal vector to the plane, but personally I would just use the fact that a plane can also be written as r.n=d so the normal vector is just (2,1,2)

One question I have is why don't you have to use a unit normal vector?

If you put in x=y=0 then you see the plane crosses the z-axis at 2, then do similar things to get it crosses the x-axis at 2 and the y-axis at 4 then do a sketch.

I'm not too sure what he's done with that cross product either! He must be doing it to find a normal vector to the plane, but personally I would just use the fact that a plane can also be written as r.n=d so the normal vector is just (2,1,2)

One question I have is why don't you have to use a unit normal vector?

Thanks Bezza, I edited my post while you were obviously replying and realised my mistake with my initial question. Thanks for the explanation of the limits.

I'm glad someone else is confused with his last method. I used the unit normal vector method but I wasn't entirely sure about the limits and ended up with 64/9 which isn't right! grrrr

he has projected the area onto the xz plane...so he can use the simple limits. To project it onto the plane you use: dxdz = |dS|U.j/|U| where U is some normal vector to the plane of interest.

|dS| = dxdz|U|/U.j

or dS = |dS|U/|U| = dxdzU/U.j

and because U.j in this case = 1, he has validly used (2,1,2)dxdz

that make any sense?

you can not use (unit vector)dxdz because dxdz is not the valid area element size....you must take into account it is a projection. He has projected the plane onto the xz-plane and used the suitable limits.

|dS| = dxdz|U|/U.j

or dS = |dS|U/|U| = dxdzU/U.j

and because U.j in this case = 1, he has validly used (2,1,2)dxdz

that make any sense?

you can not use (unit vector)dxdz because dxdz is not the valid area element size....you must take into account it is a projection. He has projected the plane onto the xz-plane and used the suitable limits.

Right now I'm so confused! I tried projecting it, the way I know how and got the annoying answer of 8/3...I'm getting closer! Could someone point out where I've gone wrong in my working? Thanks:

Project onto xy plane.

F=(0,2x,z) but z=0 therefore F=(0,2x,0)

Sec gamma = (2,1,2)/[|(2,1,2).(0,0,1)|]

sec gamma = (1,1/2,1)

Now F.sec gamma = x

Then we know the limits are:

x: 0 -> (2-y/2)

y: 0 -> 4

So Integral (0->4) Integral (0->(2-y/2)) x dxdy

Which when I evaluate it gives me 8/3!

HELP!

Project onto xy plane.

F=(0,2x,z) but z=0 therefore F=(0,2x,0)

Sec gamma = (2,1,2)/[|(2,1,2).(0,0,1)|]

sec gamma = (1,1/2,1)

Now F.sec gamma = x

Then we know the limits are:

x: 0 -> (2-y/2)

y: 0 -> 4

So Integral (0->4) Integral (0->(2-y/2)) x dxdy

Which when I evaluate it gives me 8/3!

HELP!

have you remembered to evaluate the other sides of the tetrahedron? you have successfully found the surface integral of the side defined by the plane: 2x+y+2z=4

you must now find the surface integrals of the remaining sides. Since they are all on the xy-xz-yz planes you dont have to worry about any projections, just use the suitable limits.

you must now find the surface integrals of the remaining sides. Since they are all on the xy-xz-yz planes you dont have to worry about any projections, just use the suitable limits.

Willa

have you remembered to evaluate the other sides of the tetrahedron? you have successfully found the surface integral of the side defined by the plane: 2x+y+2z=4

you must now find the surface integrals of the remaining sides. Since they are all on the xy-xz-yz planes you dont have to worry about any projections, just use the suitable limits.

you must now find the surface integrals of the remaining sides. Since they are all on the xy-xz-yz planes you dont have to worry about any projections, just use the suitable limits.

Yeah I've done all the other sides and agree with the workings Rich E put up earlier and get a total of -8/3 for the other 3 sides. Therefore, when I sum those 3 sides with this last side I get zero!!! which I know is wrong as a) it disagrees with everyone else, b) it disagrees with the next bit of the question! ARGHHH!!!!!!!!!!!!!

EDIT: I'm guessing it's my limits when I'm projecting into the xy plane that is causing the trouble...but I'm soo confused now!

Hoofbeat

Thanks Rich. But a few questions:

1) How did you know when you were working in the z=0 (or xy) plane that the limits of z are 0->2? I understand how you got the limits for x.

2) On the second page, I'm not entirely sure what you're doing! Sorry! Are you doing a cross product to get an area? Can't you just define say G = 2x + y + 2z and then find the unit normal from grad G/|grad G|? but then I'm not sure how the limits would work?

1) How did you know when you were working in the z=0 (or xy) plane that the limits of z are 0->2? I understand how you got the limits for x.

2) On the second page, I'm not entirely sure what you're doing! Sorry! Are you doing a cross product to get an area? Can't you just define say G = 2x + y + 2z and then find the unit normal from grad G/|grad G|? but then I'm not sure how the limits would work?

1) For the z=0 plane then you don't need the limits do you? As the field.normal is zero anyway. Not sure which part of my answer you're talking about.

2) The way I did the upper face's flux was to use

dS = r_u x r_v du dv

for a normal vector with magnitude of infinitesimal area. I guess it all depends how you've been taught. It being a plane it's obvious that (2,1,2) is normal (from the r.n=a.n formula), but I was taught to take dS in F.dS as the above.

The limits for the upper face depend on what parametrisation you take. You need to cover that face with two co-ordinates and the limits are whatever they need to be to achieve that. I'm using the co-ordinates (x,z) and these need to vary over the range x,z>=0, x+z <=2.

RichE

Do you guys only ever work out the flux across planar surfaces then?

Yes usually using a suitable co-ordinate system it can be reduced to a fairly simple integral (such as sphere or cylinder, as Willa said [I think]). But we would generally use the grad f/(|gradf|.n) to find sec gamma.

(Can we use LaTeX markup on these forums?)

Hoofbeat

Yup...I just don't know how to!

So what are the tags?

EDIT: Or are you saying you don't know? Let me try.

$\hat{H} | \psi \rangle = i \hbar \frac{\partial}{\partial t} | \psi \rangle$

do [ tex ] and tags (without the spaces) and use symbols as given by: http://www.fi.uib.no/Fysisk/Teori/KURS/WRK/TeX/symALL.html

so to do an alpha sign use: \alpha

also it's useful to know how to do superscript...which is just: ^{this is superscript}

subscript is: _{this is subscript}

fractions are useful as well: \frac{enumerator}{denominator}

it's best if you just experiment to see what works!

so to do an alpha sign use: \alpha

also it's useful to know how to do superscript...which is just: ^{this is superscript}

subscript is: _{this is subscript}

fractions are useful as well: \frac{enumerator}{denominator}

it's best if you just experiment to see what works!

$\hat{H} | \psi \rangle = i \hbar \frac{\partial}{\partial t} | \psi \rangle$

And that was the time-independent Schrödinger equation, ladies and gents. It's not a pretty font though. They have a better engine on www.physicsforums.com (hint hint mods).

And that was the time-independent Schrödinger equation, ladies and gents. It's not a pretty font though. They have a better engine on www.physicsforums.com (hint hint mods).

LennonMcCartney

And that was the time-independent Schrödinger equation, ladies and gents. It's not a pretty font though. They have a better engine on www.physicsforums.com (hint hint mods).

yeah, that does look a lot nicer. theres a thread in about on the latex so try posting in there

Bezza

yeah, that does look a lot nicer. theres a thread in about on the latex so try posting in there

I am a member of physicsforums. Unfortunately, it's home to a lot of crackpots who try and prove collective consciousness stuff, and refute relativity. Fortunately it's also home to a couple of geniuses.

http://www.thestudentroom.co.uk/t91246.html is the thread I was talking about. It was pig who implemented it so if you ask him nicely he might be able to change it.

- Start studying hard in Uni too late for my career?
- Thoughts from a recent Oxford Physics Graduate; Ask me anything!
- Smartest group(s) among these...
- Is it possible to do a masters in maths after an undergraduate in natural sciences
- Any astrophysicist a level
- Dropping out of physics degree to do management at warwick
- Question about Oxford Maths
- Physics and Philosophy, Oxford
- UCAS Clearing 2023 FAQ and Help Megathread
- Got a Ucas or results related question? Ask a Clearing and Applications Advisor here
- St Andrews vs Oxbridge
- AS/A-Level Physics or English Lit? I have no idea what to pick.
- Which exam board for further maths is “easiest”/how do they differ?
- 24 Years old, returning to A-Levels. Need some advice. (Physics & Maths)
- What GCSE subjects to choose to become a physicist?
- Maths//Physics work experience
- How much Physics in chemical engineering?
- Can low tier unis reject you because they think you're applying for Oxbridge?
- Law at Queen Mary University of London (QMUL) opinions?
- Chemistry or Chemical Physics?

- Oxford PPE Interviews for 2024 entry
- Mat 2023
- Human Sciences Oxford applicants 2023-2024
- Fine Art at the Ruskin Oxford 2024
- Hat 2023
- Oxford Economics and Management Interview 2024
- 2024 Oxford New College Interview Invites
- Oxford language applicants - 2024 entry
- Oxford maths interview
- TSA Section 1 2023 / Oxford E&M (2024 entry) thread
- Extra MAT 2023
- Oxford Interviews 2024 History of Art
- Oxford University Law Interview Shortlisting
- Oxford Chemistry interview questions
- John Locke Essay Competition 2023
- Oxford interviews 2023
- When will I hear back from Oxford about interviews?
- do colleges send all interview invites on the same day?
- Oxford Interview Notification
- Oxford history written work

- Dropping out of uni and reapplying
- Official Uni of Bath Applicants 2024 Entry Thread
- FTI Consulting 2024 Grad Schemes
- Has anyone heard back from UCL?
- Mature Student needing advice about what to study
- Confused on where I should apply
- The daily Wordle puzzle thread!
- Network Rail Graduate 2024
- Should I drop A-level computer science?
- Further Maths A-level *urgent

- Welcome to the Bangor University A100 2024 Entry Discussion.
- ATAS certificate for UK for January 2024 intake
- Official: University of Cambridge A100 2024 Entry Applicants
- University of Oxford 2024 Undergraduate Applicants Official Thread
- Accenture 2023-2024 grad scheme
- ATAS (Academic, Technology, Approval Scheme) Certificate 2023/2024
- PAT 2023 / for 2024 entry forum
- Official: Edge Hill University A100 2024 Entry Applicants
- Reapplying to Cambridge medicine
- history a-level coursework

- Exeter Law with French Law
- Tenancy takeover
- Land Economy 2024 Entry
- Anyone know what this tv show or movie is please
- CTAM: Count to a million (Part 78)
- Natwest 2024 Graduate Scheme
- Frontline Social Work 2024
- EY graduate scheme 2024
- Last Person To Post Here Wins (Part 54)
- do guys actually like bigger girls? be honest

- Why can't I get wet?
- DWP EO work coach Kent 602 campaign September 2023
- Volume
- Spliced and diced - perhaps one day, a little shredded!
- What to put in UCAS extra activities
- I'm 7.3 Inches is this good?
- Medicine Interview Discussion 2024 Entry
- Favourite Christmas episode in a TV show or series?
- London accommodation
- PWC graduate programs 2024