1. The problem statement, all variables and given/known data I would like to ask for Q5b function G & H 2. Relevant equations answer: G: -2pi H: 0 by drawing the vector field 3. The attempt at a solution the solution is like: by drawing the vector field, vector field of function G is always tangential to the circle in clockwise direction, so line integral is -2pi; vector field of function H is always perpendicular to the circle, so line integral is 0. the definition of flux is the vector field crosses the designated area, "perpendicular" should be crosses while "tangential" is just touching the circle, isn't it? I am now really confused with how can we visualize the equations with their physical meaning behind in order to obtain the answer... can anyone help me in clarifying the concept? thank you so much!