*11*

*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 ...

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