Because the current in a wire is a directed quantity, we need to define the
direction represented by a positive value of the variable i(t). In the same
way, the charge configuration on a capacitor is a directed quantity, and we
need to define the direction represented by a positive value of the variable
q(t). If you want to make the current represented by i(t) a vector, I can
just as easily make the charge separation represented by q(t) a vector. In
fact I don't need to invent a new vector, I could simply refer to the
direction of the dipole moment of the charged capacitor (a REAL vector) and
show its positive meaning by +/- signs on the plates.
Bob Sciamanda
Physics, Edinboro Univ of PA (Em) http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "John Denker" <jsd@av8n.com>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Monday, February 20, 2006 2:14 PM
Subject: [Phys-l] current vector
|A vector has direction and magnitude.
|
| Here's how I test to see if something is a vector. If it
| makes sense to ask "in which direction" it's a vector.
|
| If you tell me the temperature is 22 C, it would not make
| sense to ask "in which direction". Temperature is not a
| vector.
|
| If you tell me the current is 22 A, it *does* make
| sense to as "in which direction". It may be easy to
| answer the question, but that does not make the question
| or the answer any less important. Often the first half
| of the answer is "in the direction along the wire" but
| even that is not the whole answer; there is still one
| more bit of information needed (left/right or up/down
| or to/fro or whatever).
|
| I was absolutely not kidding when I said you need to draw
| the circuit diagram and mark on it a basis vector for each
| current of interest. The current vector is then some
| multiple (some scalar multiple) of this vector.
|
| If you want to focus attention on the scalar component you
| get by projecting the current onto this basis vector, that
| is fine -- and indeed computationally convenient -- but
| conceptually "the" current is still a vector, and still has
| a nontrivial direction as well as magnitude.
|
| By way of analogy, I won't object if you say the acceleration of
| gravity is 9.80 m/s^2 ... but you'd better not object if I say
| it is 9.80 m/s^2 _times a unit vector in the down direction_.
|
| In the laboratory, gravity is always in the same direction, and
| for a long straight wire, the current is always in the same
| direction ... so in the simplest cases we are talking about
| vectors in one dimension, which are rather atypical vectors,
| but still they satisfy all the vector-space axioms. And more
| importantly, thinking of them as vectors is obligatory as soon
| as you consider more interesting applications:
| -- In orbital mechanics, the g vector points in different
| directions at different places.
| -- When computing the magnetic field of a current loop, the
| current vector points in different directions at different
| places.
| -- Similarly if I consider a cubical parcel of copper inside
| a much larger chunk, and you tell me there is a current of
| 22 A flowing through that parcel, I am well within my rights
| to ask "in which direction". There are many inequivalent
| possible answers.
|
| Vern Lindberg wrote:
|
| > Current is a vector????? Current density is, but not current.
|
| What then is the current in a wire?
|
| Wires do not have zero cross-sectional size; what they really
| carry is a bunch of current density distributed across their
| cross-section.
|
| I think of a current as just a little bundle of current density.
|
| ============
|
| FWIW I consider terms like "flux of current" to be redundant in
| a mostly-harmless way. Flux means "flow" and current means "flow".
| Therefore the flux of current is just the current. The flux
| density of current is just the current density.
|
| momentum is a vector ...... momentum density is a vector
| current is a vector ...... current density is a vector
|
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