Static Fields: Fall-2025
HW 09 Practice: Due W5 D3

1. Divergence Estimate Suppose \(\boldsymbol{\vec\nabla}\cdot\boldsymbol{\vec F} = xyz^2\).
   1. Find \(\boldsymbol{\vec\nabla}\cdot\boldsymbol{\vec F}\) at the point \((1,2,1)\).
      Note: You are given \(\boldsymbol{\vec\nabla}\cdot\boldsymbol{\vec F}\), not \(\boldsymbol{\vec F}\)!
   2. Using your answer to part (a), but no other information about the vector field \(\boldsymbol{\vec F}\), estimate the flux out of a small box of side \(0.2\) centered at the point \((1,2,1)\) and with edges parallel to the axes.
   3. Without computing the vector field \(\boldsymbol{\vec F}\), calculate the exact flux out of the box.
2. Divergence

   

   Shown above is a two-dimensional vector field.

   Determine whether the divergence at point A and at point C is positive, negative, or zero.