Magnetic monopoles and Maxwell's equations in N dimensions

The possible existence of “magnetic charge” has been widely investigated in the last two centuries, since it would allow to symmetrise Maxwell's equations and to explain charge quantization. Though, notwithstanding many studies and experiments, nowaday (2013) magnetic monopoles have never been observed. In this paper we are going to show that E and B fields exhibit very different natures, but while this is not so explicit in 3 spatial dimensions (3-D), it becomes clear in a generic number of dimensions (ND). In particular, the N-D extension of cross product and curl brings to N-D Maxwell's eq.s and to reinterpret magnetic field B, explaining the probable lack of magnetic monopoles.