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Am i doing this right?

  1. Jan 27, 2004 #1

    jlmac2001

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    Here's the question:

    Suppose we have a scalar field phi(r)=xy defined on the plane (x,y). Find th vector field gradient phi, and plot the result in a single graph atthe four points (1,1), (-1,1) (1,-1), (-1,-1) and at the four points (1,0),(0,1),(-1,0) and (0,-1).

    Ans.

    For the gradient of phi(r)=xy, I got yi + xj. Is this right?
     
    jlmac2001, Jan 27, 2004
  2. jcsd
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  3. Jan 27, 2004 #2

    jlmac2001

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    one more questio

    how will I plot it. Do i have to solve the eequation at each of those points and plot the answer that I get?
     
    jlmac2001, Jan 27, 2004
  4. Jan 27, 2004 #3

    Tom Mattson

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    Yes.
     
    Tom Mattson, Jan 27, 2004
  5. Jan 27, 2004 #4

    Tom Mattson

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    Re: one more questio

    No, it's not that involved. For each of the 4 points, you plug in the values of x and y (edit: plug them into the gradient). From those, you will get 4 vectors, which you need to sketch on the graph.
     
    Tom Mattson, Jan 27, 2004
  6. Jan 27, 2004 #5

    jlmac2001

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    is this right ?

    Okay. So at (1,1) it would be i + j
    at(-1, 1)= -i
    at (1,-1) = i-j
    at (-1,-1) = -i-j

    How would I plot it?
     
    jlmac2001, Jan 27, 2004
  7. Jan 27, 2004 #6

    Tom Mattson

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    Re: is this right ?

    Right.

    These are wrong. Remember that for your vector v, grad(v)=yi+xj.

    This one is OK.

    Go to the point in question and let that be the origin of a vector whose components are what you calculated them to be. For instance, in the first case go to the point (1,1) and draw the vector i+j.

    Also, don't forget to do the same for the other 4 points listed. You will have 8 vectors in all.
     
    Tom Mattson, Jan 27, 2004
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