I'm currently in an introductory electricity and magnetism course, and I've been pondering magnetic monopoles. We didn't go in depth with them at all, but the professor made a comment when discussing Gauss's Law for Magnetism, ##\oint \vec B \cdot d \vec A=0## (can't figure out how to type a closed surface integral, as it should be), that this is a mathematically equivalent way of saying that there are no magnetic monopoles. Why exactly is this? As Gauss's Law states, the sum of the flux across a closed surface must equal zero. Is it as simple as the idea that the net flux of a magnetic monopole would not equal zero? I'm a bit confused by this. Flux is essentially the 'number' of field lines passing through a given surface. In a normal dipole, magnetic field lines essentially take the form of loops passing through the point from which they are emanating. With a magnetic monopole, magnetic field lines are radial and emanating straight out in every direction, correct? Using that fact, we can say that net flux is -not- equal to zero because field lines are not passing back through the surface? I'm still a bit confused on this idea, and I haven't been able to find much in the searching that I've done. Could anyone provide any insight?