Cancellation in Opposed Windings

Assuming you mean one of the signals is inverted before being fed into the conductor.

In the near field you have the canceling currents, in the far field the uncanceled currents

So yeah, at distance the magnetic field will be dominated by the 100kHz.

It's like from a distance the two conductors blur into one and the currents sum leaving only the 100kHz visible.

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At large distances, there will be a 1/r falloff B field which is entirely 100 Hz. At shorter distances, there will be a 1/r^2 falloff B field which has dipole character, and is 1 kHz plus 2 kHz. And inbetween the wires, there will be a field which is higher in amplitude (because both wires' B contributions add), 1 kHz plus 2 kHz.

B field doesn't 'radiate', though; it'll be bunches of loops, as always.

Thank you. That ws a very concise answer. May I clarify a few points?

Moving outwardly from the wires, what would be considered to be the starting point of a "large" distance in this context?

What is the significance of the 1KHz plus 2KHz field? Are you saying it is confined to a short distance by virtue of the cancellation process?

What is it about the latter that determines it is not 1/r?

Robert Stevens

** Huh ???

How can currents oppose in independent wires ? If you must post absurd hypotheticals, at least get your terminology right.

.... Phil

The signals are as described above. Only the 100Hz of one is inverted. Consequently, it adds with the non-inverted one when the currents of the two signals oppose "around" the conductors.

The 1KHz and 2KHz, which are in phase relative to both signals, cancel.

When I say "oppose", I mean that the current in each signal is flowing against each other in adjacent wires.

OK. Thanks.

Robert Stevens

If the wire-to-wire spacing is 'd', perhaps 4*d for both the dipole-like and the 1/r terms. In very-close-up, one could even expect nonuniformity of current density inside the radius of the wires.

It only cancels at a distance; in the space between the outbound and the return wire, it reinforces, rather than cancelling (and in that space, where 'r' is zero, an 'r' dependence makes no sense).

The approximation of '1/r' dependence belongs to very-long wires, on distance scales where the ends of the linear run are farther (maybe 4 times farther?) than the 'r' value. We know that the long-wire net current is zero (except 100 Hz), so the

1/r contribution at 1kHz+2kHz is zero at distance. Close up (compared to the interwire spacing) and very far (compared to the end-of-linear-run) these approximations don't apply.

Thank you for clarifying those points.

I had in mind that the wires were in contact, and mentioned in my OP that, for discussion purpose,s the cancellation of opposing fields was complete.

Of course I know this could never be achieved in practice.

Robert Stevens