\b[No scalar potential exists on the full three-dimensional domain.] A sufficiently smooth <gradient field> has zero <curl>, since mixed <partial derivatives> commute. The calculated <curl> is not identically zero. The fact that it vanishes at some individual points does not make the whole field a <gradient field>.

Solution

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2006 / Paper 1 / 4 / c / Solution

 Solution (source code)