Ever-increasing amplitude of the induced impulse?

[Ronnu]

Hey

I got a little imaginary experiment which is little bit confusing to me. Maybe somebody with knowledge in signal transmitting or just good knowledge of physics can help me out.

So let's say there are two parallel conductors which length is endless and resistance is zero (no losses and voltage and current are in phase with each other). One of the conductors will be connected to a signal generator which creates a single impulse which then travels along the conductor. The impulse length is a lot smaller than the distance between the parallel conductors.

The impulse that travels along one of the conductors (let's say conductor nr. 1) can be looked as a moving charge. We know that a moving charge generates magnetic field around it and that this magnetic field wave propagates perpendicular to the conductor and with the speed of light. So in some time it will propagate to the other conductor (nr. 2 ) which is next to the propagating conductor (nr. 1). According to the induction law it will generate a voltage or in another word the same impulse (although with a smaller amplitude) that was flowing in the conductor number one.

This generated impulse will start to travel along that conductor also with the speed of light. So it should be that this generated impulse is always in phase with a magnetic field that is generated by the conductor nr. 1 and that reaches conductor nr. 2. From that it should be that the amplitude of the generated impulse in conductor nr. 2 is increasing as it travels down the conductor (magnetic field that passes through the conductor induces voltages and there are no losses). This is where I get lost, because if the conductors length is endless then the amplitude will increase endlessly and that cannot be. So what am I missing?

 

[tech99]

Hey

I got a little imaginary experiment which is little bit confusing to me. Maybe somebody with knowledge in signal transmitting or just good knowledge of physics can help me out.

So let's say there are two parallel conductors which length is endless and resistance is zero (no losses and voltage and current are in phase with each other). One of the conductors will be connected to a signal generator which creates a single impulse which then travels along the conductor. The impulse length is a lot smaller than the distance between the parallel conductors.

The impulse that travels along one of the conductors (let's say conductor nr. 1) can be looked as a moving charge. We know that a moving charge generates magnetic field around it and that this magnetic field wave propagates perpendicular to the conductor and with the speed of light. So in some time it will propagate to the other conductor (nr. 2 ) which is next to the propagating conductor (nr. 1). According to the induction law it will generate a voltage or in another word the same impulse (although with a smaller amplitude) that was flowing in the conductor number one.

This generated impulse will start to travel along that conductor also with the speed of light. So it should be that this generated impulse is always in phase with a magnetic field that is generated by the conductor nr. 1 and that reaches conductor nr. 2. From that it should be that the amplitude of the generated impulse in conductor nr. 2 is increasing as it travels down the conductor (magnetic field that passes through the conductor induces voltages and there are no losses). This is where I get lost, because if the conductors length is endless then the amplitude will increase endlessly and that cannot be. So what am I missing?

The pulse on wire 2 will gradually increase until it is almost equal to the pulse on wire 1. The pulse on wire 2 is of opposite phase to that on wire 1. Wire 1 will have donated energy to the new pulse, so that the two are nearly equal but of opposite phase.

 

[Ronnu]

I don't quite understand why it's in a opposite phase. And why wouldn't the impulse on wire 2 grow any further? Also, wouldn't those two impulses be physically apart from each other (not adjacent to each other) as one "lags" little bit?

Thanks for your reply!

 

[tech99]

I don't quite understand why it's in a opposite phase. And why wouldn't the impulse on wire 2 grow any further? Also, wouldn't those two impulses be physically apart from each other (not adjacent to each other) as one "lags" little bit?

Thanks for your reply!

For close spaced wires, when a voltage is applied to line 1, a current starts to flow and a back EMF is created, by Lenz's Law, in Wire 2. The current impulse on Wire 2 must be in a direction so that its magnetic field opposes that in Wire 1.
As it grows, the impulse on Wire 2 will transfer energy back to Wire 1, until such time as equilibrium is obtained, so it will not grow for ever.
If the spacing is large compared to the wavelength, then I agree there can be a time delay (phase shift). This will correspond to the eventual mode being a mixture of the ordinary two-wire TEM and the "single wire" TM modes.
May I comment that, so far as I am aware, a magnetic field is not known to travel at the speed of light. Only an EM wave can do that. But please correct me.

 

[Ronnu]

Thanks for the reply, I can understand little bit better now how the electir field vector would be acting on the generated impulse on wire 2. But if the distance between the two wires would be the same as the length of the impulse would the eventual mode be still mixture of TEM and TE?

I think you misunderstood me about magnetic field traveling at the speed of light. I know that magnetic field itself cannot "travel", it can only exist statically as changing magnetic field always includes a changing electric field. So when I said magnetic field traveling at c I was really referring to the magnetic field that is part of the EM radiation that would propagate from the wire.

 

[tech99]

If the wires are widely spaced, in the order of a wavelength apart for this case, then some E-field lines of force originating from a position on one wire will terminate on the other wire, giving a TEM mode, but others will terminate further along the same wire, giving a single wire TM mode.