Suppose an electric field in a region of space is given by (1) where t is a constant with units of time and bis some given constant. (a) what are the units of the constant b.? sketch the e-field in the x-y plane (by hand), and then check yourself with mathematica (hint: vector is a built in command. use mma to learn the syntax, and include your mma plot with your homework.) (2) (b) calculate the closed line integral e. al where l is a circle of radius r, parallel to the x-y plane, centered at (0,0,2). integrate counterclockwise as viewed from "above". (i. e. viewed from +z) (c) calculate the closed line integral equation (2) again, this time where l is a rectangle (sides of length a and b, centered around the origin) oriented parallel to the x-y plane. (again, integrate counterclockwise as viewed from "above") clearly describe in words how the value of equation (2), here and in part (b), depends on b./t and the geometry of l. (d) calculate v x e and describe the resulting vector field in words. show that the closed line integral values in (b) and (c) are equal to the corresponding surface integrals of v x e. relate this to stokes' theorem! (e) determine the scalar potential that gives equation (1) (or explain why no such potential exists.) finally - describe how you could use such a static electric field to make a lot of money and save the world. does the electric field in this problem violate any of maxwell's equation for a static situation?