Conservative Vector Field: Finding the Value of 'a

[hils0005]

Homework Statement

For what value(s) of the scalar 'a' is the vector field
F(x,y,z)= 2xz i + ay^3 j + (x^2 + y^4) k conservative

The Attempt at a Solution

F1=2xz
F2=ay^3z
F3=(x^2 + y^4)

I used 3D curl test??

1)(partial F2)/(partial dx) - (partial F1)/ (partial dy)= 0-0 = 0
2)(partial F3)/(partial dy) - (partial F2)/ (partial dz)= 4y^3 - ay^3=0 so a=4
3)(partial F1)/(partial dz) - (partial F3)/ (partial dx)= 2x-2x = 0

my answer would be a=4

 

[Defennder]

If your Fy is supposed to be ay^3z then you're right. Your initial statement of the problem has Fy = ay^3.

 

[hils0005]

yes it should be ay^3z j, Thanks!