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Divergence problem

  1. Jan 26, 2016 #1
    So I have this problem which wants me to find the divergence of:
    \begin{equation}
    \vec{B}(x,y,z) = (x^3+y^2z)\hat{x}+(y^3+x^2z)\hat{y}
    \end{equation}
    Given that the divergence is given by:
    \begin{equation}
    \nabla \cdot \vec{B} = (\hat{x}\frac{\partial}{\partial x}+ \hat{y}\frac{\partial}{\partial y}) \cdot (B_x \hat{x} +B_y \hat{y} ) = \frac{\partial B_x}{\partial x} + \frac{\partial B_y}{\partial y}
    \end{equation}
    By doing that I get:
    \begin{equation}
    3x^2+3y^2
    \end{equation}
    I feel like the answer should be a scalar, can someone give me a hint if I am doing the correct steps, or provide me a hint on where I am going wrong?
     
  2. jcsd
  3. Jan 26, 2016 #2

    RUber

    User Avatar
    Homework Helper

    ##3x^2 + 3y^2 ## is a scalar. It is just a different scalar at any given point in the plane.
     
  4. Jan 26, 2016 #3
    Why do you believe your answer isn't a scalar?
     
  5. Jan 26, 2016 #4
    Ah, yes, you're right, I forgot that I got rid of the \hat{x} and \hat{y} when I took the dot product.

    Thank you! :)
     
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