8. (10 points) Let R be a bounded region in space with regular surfaces E1, ..., Ex as boundary compo- nents. Let y be a differentiable function on R satisfying: " is harmonic, i.c. Ay =0 . "x, = Cie. y is constant on each boundary component. " is non-constant on R. Prove that B := Vy is divergence free but not solenoidal (the field in problem 8 midterm II was exactly of this type)