Example problem in a math analysis class.

Maxwell's equations are a set of four partial differential equations that form the foundation of classical electrodynamics, classical optics, and electric circuits. Maxwell's equations describe how electric and magnetic fields are generated and altered by each other as well as by charges and currents. These fields underlie modern electrical and communications technologies. One of these equations, Gauss' law of magnetism, is given as follows: V . B = 0 a. Based on what we know about divergence, what does the equation above tell us about the presence of sources or sinks in the magnetic field, B? b. Determine if the following magnetic fields conform to Gauss' law of magnetism: - B = [r2z3, 2r2, zsine] - B = [xsinzy, cosxy, zsinxy] - B = [0, r, -rocos0] (in spherical coordinates)