Line, surface and volume integrals
11.1 The vector field F is defined by
Calculate ∇ × F and deduce that F can be written F = ∇ϕ. Determine the form of ϕ.
With F as given, we calculate the curl of F to see whether or not it is the zero vector:
The fact that it is implies that F can be written as ∇ϕ for some scalar ϕ.
The form of ϕ(x, y, z) is ...