A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the magnetic force experienced by the moving charged particle can be described by the vector field 1 F(x, y) = NI y?it5x2j. (a) Evaluate F(0,1), F(1,0), F(0,2), F(2,0), F(1,1), F(2,2), F(1,2), F(2,1). (4 marks) (b) Describe F by sketching the vectors from Question 6(a) in the first quadrant plane. (4 marks) (c) Determine if F is a conservative vector field. (2 marks)(d) Given that the charged particle is moving along the straight line from (3, -3) to (0, 3), as represented by the solid line in the figure below. (0, 3) (0, 0) (3, -3) Figure Q6(d) Calculate the work done by the magnetic force given by the integral F.dr , Jc where C is the straight line from (3, -3) to (0, 3). (5 marks)(e) Now, consider the polygonal region with vertices (0, 3), (0, 0) and (3, -3) as shown in the figure above (the region bounded by the dotted and solid lines), use Green's Theorem to calculate the work done F. dr C where C is the straight line described in Question 6(d)