Question 2 Define a force field (in Newtons) by T 2y 2x F(x, y) = x + 1+x²y² 1 + x²y² where coordinates x and y are in meters. (a) Evaluate F(1, 0), F(0, -1), F(1, 1), F(-1, -1) and sketch them on the xy-plane. (8 marks) (b) (c) (d) Show that the force field is conservative and hence evaluate a scalar potential function E(x,y) such that F = VE. (9 marks) A path C is parameterized by the function below. Calculate the work done by F(x, y) along the path C. [t- r(t)= = 0 <t≤1. 1 (5 marks) With reference to the vector field, explain why the work done in part (c) is positive (or negative). (5 marks)

Fig: 1