Divergence problem

  • #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?
 

Answers and Replies

  • #2
RUber
Homework Helper
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##3x^2 + 3y^2 ## is a scalar. It is just a different scalar at any given point in the plane.
 
  • #3
944
394
Why do you believe your answer isn't a scalar?
 
  • #4
##3x^2 + 3y^2 ## is a scalar. It is just a different scalar at any given point in the plane.

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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