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I would like to know if the shape of the magnetic field around twisted pair insulated wires will be a helical shaped magnetic field if both wires have parallel electrical current running through them.

For example, say that two ends of the twisted pair wires are touched to the positive terminal of a battery and the other two ends of the twisted pair wires are then touched to the negative terminal of the battery so that there will be parallel electrical currents flowing through the two wires.

I have spent the last two days using Google to search the Internet for what the shape of the magnetic field is around twisted pair wires with parallel electrical currents, but so far I have not found any illustrations or drawings of this particular magnetic field, so I am hoping that someone here on Physics.SE will answer this for me.

Do twisted pair wires create a helical shaped magnetic field if parallel electrical currents are run through the two wires?

EDIT

I asked the wrong question concerning my inquiry. The question I should have asked is, "Do magnetic field lines surrounding twisted pair wires follow a helical path along the length of the twisted pair wires if parallel electrical currents are run through the two wires?". I am considering asking this question in a new post.

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"Helical" might be a correct name for this magnetic field shape, but it's an unusual name.

Let's think about the usual physics-cartoon picture of a solenoid:

a solenoid

Most treatments are focused on the field inside of the solenoid, and start from the assumption that the solenoid is very long and that the coils are very close together. This field is parallel to the solenoid's central axis. But a solenoid of finite length has the mostly-axial return field on the outside. And near a solenoid where the current goes in one end and out the other, as in this illustration, there will be a small amount of the circumferential straight-wire field, because there is nonzero current flowing parallel to the axis, from the right side of the figure to the left side.

So let's imagine making your parallel-twisted-pair cable in the following way. Start with two parallel wires, like you might pull out of a ribbon cable. If they are straight, the magnetic field will (mostly) be the circumferential straight-wire field. Take your parallel-wire cable and wind it around some dowel into a solenoid: now the field is mostly the solenoidal field, strong in the core of the coil, with a weaker return field outside, and only a tiny bit of the circumferential field. Now remove the dowel and pull the coiled cable straight: the twists will remain, generating a twisted-pair cable. As the "coils" get farther apart, the axial return field gets weaker, while the circumferential field stays the same. This does in fact give you a helical field, with both circumferential and axial components; you can tune the "angle" of the helix by tuning the tightness of the twist between the two wires in the cable.

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