-t. Hint: cos = 1+cos 0 2 . Exercise 3 Vector potentials. Certain vector fields are generated by taking the gradient of a function (a) Compute the 2D vector field generated by the potential o(x, y) = 1 (b) There are ways to check if a vector field was generated by a vector potential. Namely, given a vector field Vo? Namely, in 2D, it means that F = (f, g) = (x, y). F, the question is, is there a o such that F Consider your answer in a) and compute the derivatives dyf and org. (c) Let F = (f,g) (f,g) = (2xy, y2). Compute dyf and Org. You are told F is not generated by a vector potential. (d) Can you try to guess/explain a rule for the existence of a potential o, based on c) and d)? - Exercise 4 Escape velocity using vector line integrals. Consider a spaceship that is traveling from the surface of the Earth to space in a straight line. We are going to compute the work necessary to perform to nal field of Earth. The (normalised) gravitational force is given by: