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Homework Help: Vector field notation help

  1. Feb 12, 2007 #1
    Just a quick question about notation.

    I was given the vector field

    F = r + grad(1/bar(r)) where r= (x)i+(y)j+(z)k.
    grad is just written as the upside down delta (gradient) and the bar I wrote in the above equation looks like an absolute value around just the r (although I don't know if it is absolute value). Basically I want to find the gradient of (1/bar(r)).

    What would be a simplification of this vector field so that I can solve the rest of the problem?

    I want to find its flux across the surface of a sphere.


    I think F would be ((x^3)-1)/x^2+((y^3)-1)/y^2+((z^3-1)/z^2, but I'm not sure.
     
  2. jcsd
  3. Feb 12, 2007 #2
    [tex]|\vec{r}|[/tex] is the modulus, or magnitude, of vector [tex]\vec{r}[/tex].
     
  4. Feb 12, 2007 #3

    HallsofIvy

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    If [itex]\vec{r}= x\vec{i}+ y\vec{j}+ z\vec{k}[/itex] then
    [tex]\frac{1}{||\vec{r}||}= \frac{1}{\sqrt{x^2+y^2+ z^2}}= (x^2+y^2+ z^2)^{-\frac{1}{2}}[/tex]
    What is the gradient of that function?
     
  5. Feb 12, 2007 #4
    How can you take the gradient of the function if it doesn't have i, j, and k?

    Is it 0?
     
  6. Feb 13, 2007 #5

    cepheid

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    A better question would be, how could you take the grad of the function if it *did* have i, j, and k? Remember, the gradient acts on a scalar.
     
  7. Feb 13, 2007 #6

    HallsofIvy

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    Well, you would first have to know what "gradient" actually means!

    Given a function f(x,y,z), how would YOU define
    [itex]\nabla f[/itex]?
     
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