Past exam of the mathematics course of the University of Cambridge / 2014 / ia / Paper 3 / 3A / b / ii / Solution

In three dimensions the curl can be written with the Levi-Civita symbol:Both terms contract an antisymmetric array with a symmetric one, and therefore vanish. Every differentiable radial field of this form has zero curl away from the origin. This is the three-dimensional part of the divergence and curl of a radial vector field.