2. (10 points) The Helmholtz Decomposition for a bounded domain R implies that a divergence free field B tangent to the boundary of R is the curl of some field A ( i.c. B is solenoidal) . Find an example of a bounded region R and a divergence free field B on R perpendicular to the boundary of R which is not solenoidal. (Hint: what is the only example of a divergence free non-solenoidal field that you know ?)