1. If the vector field Ā = ây3x? + âyy – â,5z³ is given, express à in cylindrical and spherical coordinates for any point in space.

icon
Related questions
Question
Problems:
1. If the vector field Ā = âx3x² + âyy - â,5z³ is given, express à in cylindrical and
spherical coordinates for any point in space.
2. For a vector filed Ā = â,2r³ – âz2z, verify divergence theorem using the cylindrical
surface enclosing the volume defined by
4 > z > 0, 3>r > 0, 2n > ¢ > 0.
3. A vector field is given as F = â„2r² + âgr²Coso + âz5z. Verify Stokes theorem for
this vector field using the surface defined by
1<r< 2,0< ¢ <÷,z = 0
2
and the closed contour that encircles this surface.
Transcribed Image Text:Problems: 1. If the vector field Ā = âx3x² + âyy - â,5z³ is given, express à in cylindrical and spherical coordinates for any point in space. 2. For a vector filed Ā = â,2r³ – âz2z, verify divergence theorem using the cylindrical surface enclosing the volume defined by 4 > z > 0, 3>r > 0, 2n > ¢ > 0. 3. A vector field is given as F = â„2r² + âgr²Coso + âz5z. Verify Stokes theorem for this vector field using the surface defined by 1<r< 2,0< ¢ <÷,z = 0 2 and the closed contour that encircles this surface.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer