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[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