Cancel magnetic field in one current carring wire

Can anyone suggest the best way to shape a single wire carring a
current so that it's magnetic field cancels itself out? Completely if
possible. I'm trying to optimize the idea for light weight and varying
current values. All I can think of would be to bunch the wire into a
tight zig-zag plane. (From:---------- To:||||||||) Would that work? Or
would it produce the same field...and just be heavy? Any help would be
great, thanks.

 

The cancellation will be nearly complete if half of the
wire runs back along the same path as the other half.
Twist the halves together and it will be better yet. Put
a hole down the middle of one half, enlarge it, and run
the other half back thru the hole, (coaxially), and the
cancellation is as perfect as the coaxiality.

If the single wire has to carry current from one point
to another in a different place, then you are chasing
a rainbow. There will be a magnetic field created
by that current, no matter what path it takes between
the two separated points.

It would produce very nearly the same field, and just
dissipate more heat to carry the same current.

You could get better help by stating more of your
real problem and constraints.

 

You're right, I meant to mention that it had to be between two points.
Chasing a rainbow then. Are you sure? What if I wrapped it in a coil
for half the distance, then wrapped it in the opposite direction for
the other half? Like magnet/solinoid wraps. I just thought of it, but
that would change the direction of the field and cancel out right? Or
would that be the same as the zigzag? (This is for a math model that I
gave up on a while ago when I realized that I would have to create and
destroy electrons to have a single current between 2 points in a closed
system. Now this is another idea how to make it realistic...unless it's
impossible. Just trying to think and get knowledgable feedback. )

 

The only way to cancel the magnetic field of a current is to have that
current return by the same path. The best you can do is to use a
coaxial wire, with the current going out in one conductor and coming
back through the other. A twisted pair is pretty good. A twisted
quad (two wires at the corners of the cross section carrying one way,
the wires at the other two corners of the cross section carrying the
other way), is better, etc.

 

Well, I am sure that *if* you have a current not following
its own return path back coaxially, *then* there will be a
magetic field produced by that current.

Almost, but not quite. And the not quite is equivalent
to what you get if the current does no spiraling around
and just travels in a straight path along the axis of what
was the spiral.

The same in the sense of no net improvement.
Your zigzag is probably easiest to think about.
Consider that each zig or zag can be broken
into two vector components. One is in line
with the net direction of the zig-zag, the other
is transverse to it. The transverse components
of the zigs cancel the transverse components of
the zags, but the in line components all add in
the same direction, as much as would the effect
from a plain straight current flow.

Now you're on to the practical issue here. In the
world we inhabit, there is no such thing as a current
not flowing in a loop in appreciable amounts. You
can imagine single or small numbers of charges being
made to movie that way, but either they have to get
back to their source, (an ever mounting positive or
negative) region, or you have to have an unreal device
to keep moving them indefinitely.

 

Alright, if you're still following this, maybe you can think of a way
to make this work: Just think of an x-y plane where the magnetic field
is in the z direction. There are two battteries, DC generators,
whatever at two points. Say (0,0) and (10,0). If two wires are
connected between the two sources, there would be a current in both
wires. Both would generate a magnetic field and cancel out. Can you
think of a way to shape one of the wires so that it would not effect
the forces on the whole system? So that it would not produce a net
force in any direction and only the one wire (along the x-axis) would
be in the math model? (eg. I think a tall triangle would make the
effects in the y direction negligable, but then it would produce a
large effect in the +- x direction...) Any ideas? Impossible?

 

They would cancel out, if the current flows were
coaxial, at points outside the outer conductor.
If the currents are not coaxial, there will be a
net magnetic field at most points. There could
be some cancellation, along some surfaces or
lines, depending on the flow geometry.

Your question is too vague for me to understand.
Only moving charges are subject to a force due
to a DC magnetic field. And the closed system
does not exert net forces upon itself, (at least not
in the DC case. If it emits photons, it could.)

Sorry, I don't know at this point.