Let us assume that we have a very thin, square, imperfectly conducting plate 2 m on a side, located in the plane z = 0 with one corner at the origin such that it lies entirely within the first quadrant. The potential at any point in the plate is given as V = −e^−x sin y.

(a) An electron enters the plate at x = 0, y = π/3 with zero initial velocity; in what direction is its initial movement?

(b) Because of collisions with the particles in the plate, the electron achieves a relatively low velocity and little acceleration (the work that the field does on it is converted largely into heat). The electron therefore moves approximately along a streamline. Where does it leave the plate and in what direction is it moving at the time?