1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof on why del is normal to surface?

  1. Feb 1, 2013 #1
    1. The problem statement, all variables and given/known data

    Simple proof on why ∇∅ is normal to surface of ∅(x,y,z) = constant

    2. Relevant equations



    3. The attempt at a solution

    2cyrls.png
     
    Last edited: Feb 1, 2013
  2. jcsd
  3. Feb 1, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The 'attempt at a proof' is a good 'relevant equation' maybe with a little fixing. Now what's the attempt at a proof?
     
  4. Feb 1, 2013 #3
    Sorry, I attached the wrong picture!
     
  5. Feb 1, 2013 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Ok that's more like it. Now if you want to make the string of equations function as a proof you need to add some words explaining why it's a proof. What kind of a curve are you taking ##\vec s## to be? And why does the last line show grad(phi) is normal to the surface?
     
  6. Feb 1, 2013 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Let s(t) be a curve lying in the surface [itex]\Phi(x,y,z)= const[/itex].

    Show, using the chain rule, that, along that curve, [tex]\frac{d\Phi}{dt}= \frac{ds}{dt}\cdot\nabla \Phi= 0[/tex].
     
  7. Feb 1, 2013 #6
    s is the distance along the curve, t is the unit tangent vector to the curve...

    does this proof make sense?
     
  8. Feb 1, 2013 #7

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Same thing I said before. A proper proof involves at least a little narrative in words as to what things are, like you just did, and how the final equation justifies the conclusion that grad(phi) is normal to the level surface of phi. Supply those and it will work fine.
     
    Last edited: Feb 2, 2013
  9. Feb 2, 2013 #8
    Thanks! I will do that in future. The math is correct, right?
     
  10. Feb 2, 2013 #9

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Same thing I said before, again. Something like ##\frac{ d \phi }{ds}=0## is neither right nor wrong until you say how s is related to phi. But yes, you can make it work by doing that. The math is correct in that sense.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof on why del is normal to surface?
  1. Normal proof (Replies: 3)

Loading...