Ed, The direction of current in an electrical circuit has nothing to do with any coordinate system. It is defined by convention in electricity as the direction opposite to that in which the electrons are moving. So the current is indicated as being from + to - in a circuit. Of course, you may change the convention but it still will not make the current (defined as the rate of change of charge i = dq/dt) a vector quantity. Current density is not the same as current. Current density is a directional quantity defined not with respect to any convention but with respect to a coordinate axis, and any transformation in that axis would result in a transformation in the current density by the same operator. Therefore current density is a vector.
Mathematical tricks maybe, but all for a reason :) Ganesh On Thu, 14 Oct 2010 11:22:15 -0400, 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 / -- *
