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Normal vector in surface integral of vector field

  1. Jul 18, 2016 #1
    1. The problem statement, all variables and given/known data
    when the normal vector n is oriented upward , why the dz/dx and dz/dy is negative ? shouldnt the k = positive , while the dz/dx and dz/dy is also positive?

    2. Relevant equations


    3. The attempt at a solution
    is the author wrong ?
     

    Attached Files:

  2. jcsd
  3. Jul 19, 2016 #2

    BvU

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    Try a few examples and you'll see.
    Remember when vectors are perpendicular
    and when lines are perpendicular
     
  4. Jul 19, 2016 #3
    Can you give some example???
     
  5. Jul 19, 2016 #4

    BvU

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    z = x
     
  6. Jul 19, 2016 #5
    i still dont understand what do you mean, can you explain further?
     
  7. Jul 20, 2016 #6

    vela

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    The surface ##\sigma## is defined by ##\phi(x,y,z)=0## where ##\phi(x,y,z)=z-f(x,y)##, and the normal is the gradient of ##\phi(x,y,z)##. What do you get when you calculate that?
     
  8. Jul 20, 2016 #7
    why it will become like this ?
     
  9. Jul 20, 2016 #8

    BvU

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    Why don't you simply fill it in and see ? Asking 'why' forever doesn't make sense. Make a sketch for the simplest case if 4.5.1 is too complicated.
     
  10. Jul 24, 2016 #9

    vela

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    I'm sure this is covered in your textbook.
     
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