The discussion centers on the phase relationship between the magnetic field generated by a wire carrying an alternating current and the current itself. Participants explore whether the magnetic field remains in phase with the current at various distances from the wire, considering factors such as the frequency of the alternating current and the dimensions of the experimental setup.
Participants express multiple competing views regarding the phase relationship between the magnetic field and the current, with no consensus reached on whether the magnetic field remains in phase or experiences a phase shift based on distance and frequency.
Limitations include the dependence on specific experimental setups, the need for precise definitions of terms like "phase shift," and the unresolved nature of mathematical relationships involved in the discussion.
tech99 said:the dimensions of the experiment are too small for radiation to be significant
These two statements would seem to be at odds. The field propagates away from the wire at the speed of light c, so there will be a phase shift related to the frequency and the propagation distance, no?tech99 said:Or does the propagation time through free space introduce a phase shift?
Thanks for the comments so far. This was my initial assumption. However, the energy in the magnetic field is not being radiated, and does not permanently leave the wire. It is just stored, and then returns to the wire. So my idea is that equal energy flows away from and towards the wire, so there is no net outflow. So I don't think it is possible to detect a propagation delay, and it appears that the whole field at whatever distance from the wire cycles simultaneously. It seems similar to the case of the phase of a standing wave, where energy also flows both ways.berkeman said:These two statements would seem to be at odds. The field propagates away from the wire at the speed of light c, so there will be a phase shift related to the frequency and the propagation distance, no?
Thank you. Yes, agree. If the wire is driven, for instance, by a step function, the magnetic field will expand outwards at the speed of light, so there is a time delay. But if the wire is driven by a continuous sinusoid, then energy is flowing both ways equally (away from and towards the wire) so my idea is that no propagation delay can then be discerned.mfb said:Well, it depends on the scales of your setup, where d is the distance (scale) and f is the AC frequency:
##df \ll c##? -> no notable phase shift, radiative terms (you can never avoid that completely) are negligible.
##df \gg c##? -> large phase shift, radiative terms are dominant.
In between, it is complicated.
There is still a loss due to radiation, so that part of the signal does propagate away with the appropriate delay...tech99 said:But if the wire is driven by a continuous sinusoid, then energy is flowing both ways equally (away from and towards the wire) so my idea is that no propagation delay can then be discerned.
But at that distant point, there are two waves. One going outward and one coming inward. Both contain equal energy. So the phasor diagram will show the two rotating in opposite directions, and give constant phase.marcusl said:There is always a delay since information about the phase of the current travels from the wire to a distant point at the speed of light.
Where did the inward-moving wave come from?tech99 said:But at that distant point, there are two waves. One going outward and one coming inward
You should do the suggested sums yourself, based on c, and come to a conclusion. c is about 1m per 3 nanoseconds and the time period at 50Hz is 20ms. What sort of a fraction of a cycle does that represent for a distance of 10m?tech99 said:I think it will always be in phase
For an alternating current, when the current increases, the field moves outwards as it is built, and when the current decreases, the field moves inwards as it collapses.berkeman said:Where did the inward-moving wave come from?
But EM is a transverse wave, not a longitudinal wave. I guess I'm not understanding what you and @mfb are saying...tech99 said:For an alternating current, when the current increases, the field moves outwards as it is built, and when the current decreases, the field moves inwards as it collapses.
I understand your problem. What I am suggesting is that the energy flows outwards, then inwards, so there is no net flow, rather like a standing wave.berkeman said:But EM is a transverse wave, not a longitudinal wave. I guess I'm not understanding what you and @mfb are saying...
tech99 said:the magnetic field of a wire carrying an alternating current
Your OP was about the field generated by a wire, but now you are talking about coils separated by a distance? Now I'm really confused...tech99 said:So maybe if two coils of wire are separated by a distance, one driven and the other open circuit, we will not see a phase shift due to the distance.
A localized source generates only outgoing waves. An incoming wave can only be generated by an external source (think of a pair of communications antennas). The field of the source is computed by use of retarded potentials (see the wiki article) or the retarded Green function, both of which replace t by (t-r/c) as mfb pointed out.tech99 said:But at that distant point, there are two waves. One going outward and one coming inward. Both contain equal energy. So the phasor diagram will show the two rotating in opposite directions, and give constant phase.
Does not that apply only to radiated energy? Reactive energy is just stored so cannot be outflow only; net energy is not lost from the wire unless radiation takes place.marcusl said:A localized source generates only outgoing waves. An incoming wave can only be generated by an external source (think of a pair of communications antennas). The field of the source is computed by use of retarded potentials (see the wiki article) or the retarded Green function, both of which replace t by (t-r/c) as mfb pointed out.
Would it be better to say that the Energy of the Magnetic Field moves out and in? If the wire is carrying AC, the energy that exists in the fields around it will 'return' to the circuit and be dissipated in a resistive load, in the source resistance or stored in the Capacitances (or equivalent)in the system.tech99 said:For an alternating current, when the current increases, the field moves outwards as it is built, and when the current decreases, the field moves inwards as it collapses.