A point charge q (C) is located at the origin of the coordinate system. An imaginary cube of side length 2a (in meters) is centered at the origin.

a) Mostly straightforward: Express the electric field due to this charge in spherical coordinates, then convert that to Cartesian coordinates so that you can more easily set up the next part of the problem.

b) Simple in concept, but complicated in execution because of the resulting integrand: Explicitly evaluate (in Cartesian coordinates) the surface integral (flux) over the surface S defined as the face of the cube that is perpendicular to the xaxis and intersects the positive x axis. You may need to use a computer algebra system (e.g. Wolfram Alpha, available for free online) to evaluate the resulting integral.

c) An important concept: Using the inherent symmetry of the problem, verify Gauss's law by considering the total flux out of the cube.