Ed, I think you're confusing 'electric current' with 'electric current density'. The first is a scalar, the second a vector. The current I is defined as the surface integral of the density vector J with respect to the element of area dA:
I = integral over S (J.dA) (how I wish we could use proper equations in e-mails!) in other words, the net flux of the current density vector field flowing through the surface S. J and dA are both vectors, J.dA is their scalar product, hence I must be a scalar. ( Source: http://en.wikipedia.org/wiki/Current_density ). You're right that in principle definitions are arbitrary. However there exist a whole set of conventional definitions which are completely self-consistent and which we would be wise to stick to. These have been honed over many years by people who know what they're doing, and which do not lead us into logical contradictions. If you're going to come up with an alternative set of definitions you are going to have to prove to everyone that they aren't going to lead us into contradictions now and in the future. I wish you luck with your task! For example how in your definition can both the current and the current density be vectors? What is your version of the above equation that relates them? Cheers -- Ian On Thu, Oct 14, 2010 at 4:22 PM, Ed Pozharski <epozh...@umaryland.edu> wrote: > Again, definitions are a matter of choice. Under your strict version I > still may consider electric current as vector, if I introduce the > coordinate system in the circuit. When I transform the coordinate > system (from clockwise to counterclockwise), current changes direction > with it. By the way, check the *current density* - it is a vector and > it obeys, in generalized case of an inhomogeneous material, a tensor > form of Ohm's law. > > There is no "correct" definition of anything. Ian is right in the > narrow sense of the conventional vector in multiple dimensions and, > especially, regarding the software implementation. But there is a > legitimate (i.e. not self-contradictory) broader definition of a vector > as an element of vector space, and complex numbers fall under it. Math > is flexible, and there is definite benefit of consider complex numbers > (and electric current under some circumstances) as vectors. > > Checking out of semantics hotel, > > Ed. > > On Thu, 2010-10-14 at 16:47 +0200, Ganesh Natrajan wrote: >> The definition of a vector as being something that has 'magnitude' and >> 'direction' is actually incorrect. If that were to be the case, a >> quantity like electric current would be a vector and not a scalar. >> Electric current is a scalar. >> >> A vector is something that transforms like the coordinate system, while >> a scalar does not. In other words, if you were to transform the >> coordinate system by a certain operator, a vector quantity in the old >> coordinate system can be transformed into the new one by using exactly >> the same operator. This is the correct definition of a vector. >> >> G. >> >> >> >> On Thu, 14 Oct 2010 10:22:59 -0400, Ed Pozharski >> <epozh...@umaryland.edu> wrote: >> > The definition game is on! :) >> > >> > Vectors are supposed to have direction and amplitude, unlike scalars. >> > Curiously, one can take a position that real numbers are vectors too, if >> > you consider negative and positive numbers having opposite directions >> > (and thus subtraction is simply a case of addition of a negative >> > number). And of course, both scalars and vectors are simply tensors, of >> > zeroth and first order :) >> > >> > Guess my point is that definitions are a matter of choice in math and if >> > vector is defined as an array which must obey addition and scaling rules >> > (but there is no fixed multiplication rule - regular 3D vectors have >> > more than one possible product), then complex numbers are vectors. In a >> > narrow sense of a real space vectors (the arrow thingy) they are not. >> > Thus, complex number is a Vector, but not the vector (futile attempt at >> > using articles by someone organically suffering from article dyslexia). >> > >> > Cheers, >> > >> > Ed. >> > >> > >> > O > > -- > Edwin Pozharski, PhD, Assistant Professor > University of Maryland, Baltimore > ---------------------------------------------- > When the Way is forgotten duty and justice appear; > Then knowledge and wisdom are born along with hypocrisy. > When harmonious relationships dissolve then respect and devotion arise; > When a nation falls to chaos then loyalty and patriotism are born. > ------------------------------ / Lao Tse / >
