I might add that an EMF is another such directed circuit component. We use
the variable E to describe this component (in Volts) and must somehow
indicate the polarity implied by a positive value of E. In my experience +
and/or - signs are commonly written to show this choice.
Equivalently, the EMF is often written as two vertical lines of unequal
length, the longer line indicating the default positive terminal. I think
it is most customary to use both indicating methods, together. This is
probably because it is easy to forget the convention of which line (long or
short) represents the default positive terminal (I may have it wrong, above,
for all I know).
Bob Sciamanda
Physics, Edinboro Univ of PA (Em) http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "Bob Sciamanda" <trebor@winbeam.com>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Monday, February 20, 2006 2:39 PM
Subject: Re: [Phys-l] current vector
| 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
||
|| _______________________________________________
|| Forum for Physics Educators
|| Phys-l@carnot.physics.buffalo.edu
|| https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
||
|
| _______________________________________________
| Forum for Physics Educators
| Phys-l@carnot.physics.buffalo.edu
| https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
|