1. A boson inside a particle accelerator describes the path shown in the image,
in which, when accelerated in a vacuum, it rises and at the same time describes
a spin about the vertical axis (z) to which it is associated (similar to the
trajectory of a particle in a tornado), until it collides with the upper wall of
the accelerator, where it returns to the center of the z axis in a totally radial
trajectory, and when it is in the center, it descends to the bottom of the accelerator
in a straight line, to begin retrace the same path.
If an electric field modeled by:


E=[cos 0+Rªsen cos 0μ +[R² sene cos² - seno]μ₂ + Øμ¹₂

interacts with the path of the boson; you are asked to prove the fulfillment
(or non-fulfilment) of Stokes' theorem, with this field on the path described by
the boson.