Worksheet: Divergence and Curl in Cartesian Coordinates

In this worksheet, we will practice finding the divergence and the curl of a vector field in Cartesian coordinates and discussing their physical meaning.

Q1:

Which of the following is true concerning the vector field V defined by V i k ( 𝑥 , 𝑦 , 𝑧 ) = 𝑦 𝑥 ?

  • A V is a conservative vector field.
  • B V has a positive divergence at every point ( 𝑥 , 𝑦 , 𝑧 ) .
  • C V ( 𝑥 , 𝑦 , 𝑧 ) 0 , for all ( 𝑥 , 𝑦 , 𝑧 ) .
  • D V ( 𝑥 , 𝑦 , 𝑧 ) is orthogonal to the vector j 0 , 1 , 0 , for all ( 𝑥 , 𝑦 , 𝑧 ) .

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.