Induced voltage between parallel conductors/wires

[Casper Hansen]

Hello

How do I calculate the induced voltage in a passive signal cable that runs parallel to a 1 phase power cable?

Cable A is the power cable I = 500 A
Cable B passive signal cable

where:
D= 209.65 mm: distance between wires ( center wire to center wire)
r= 10 mm: radios of each wire
f=60 Hz
S=2200 m parallel length
I_rms = 500 A

First i calculate inductance [H/m]
Ls = (u0 / 2 * pi) * ln(D/r) = 6.0857 * 10^-7 [H/m]
Ls_f = Ls * 2 * pi * f => u0 * f * ln(D/r) = 2.294 * 10^-4

Vs = Ls_f * I_rms * sqrt(2) = 0.1622 [V/m]

V = Vs * S = 356.9 V

are the above calculations that the right approach?
My biggest concern is that if I increase the distance between wires S, the inductance increase as well as the induced voltage due to ln(D/r) part in the equation. I can't see why that should be true because the wire (cable B) moves farther away from the source of the B-field (cable A). I thought that the induced voltage would decrease with increased distance of the wires.

 

[anorlunda]

Is this homework?

Does the power cable include the return leg, or just one leg of the closed circuit?
Same for the signal, where is the return leg of that closed circuit?

A diagram would be helpful. You can use the UPLOAD button to insert pictures.

 

[Casper Hansen]

Is this homework?

Does the power cable include the return leg, or just one leg of the closed circuit?
Same for the signal, where is the return leg of that closed circuit?

A diagram would be helpful. You can use the UPLOAD button to insert pictures.

no, it's not homework, but something I've encountered several times now that made me think about does the induced voltage de- or increase with distance.
I have uploaded a image and diagram, see attachment.

 

[berkeman]

no, it's not homework, but something I've encountered several times now that made me think about does the induced voltage de- or increase with distance.
I have uploaded a image and diagram, see attachment.

Welcome to the PF.

While a single wire carrying a current can create a magnetic field, it takes a loop to pick up a voltage from the changes in that magnetic field. Can you post a picture or a more complete drawing of the situation? Are you familiar with Faraday's Law of Induction?

https://en.wikipedia.org/wiki/Faraday's_law_of_induction

 

[anorlunda]

I asked for a diagram and the OP provided a circuit shcematic. The schematic does not show the return line for the secondary wire to complete a closed circuit. Nor do schematics show dimensions our layout of the wires.

Here's a good tip to remember. To do circuit analysis we ignore physical layout and size (thank God) and think only of circuit topology. To do field calculations using Maxwell's equations or Faraday's laws, the size, orientation and placement and layout of the wires is the whole ball game and can't be ignored.

 

[Casper Hansen]

Welcome to the PF.

While a single wire carrying a current can create a magnetic field, it takes a loop to pick up a voltage from the changes in that magnetic field. Can you post a picture or a more complete drawing of the situation? Are you familiar with Faraday's Law of Induction?

https://en.wikipedia.org/wiki/Faraday's_law_of_induction

Thanks...

Ya i understand that a wire carrying a current create a magnet field B (magnetic flux density) and that ΦB (magnetic flux) is a product of the B and a loop area dA that enclose the B field. ( ΦB is the total magnetic flux in the area that the loop enclose).

I asked for a diagram and the OP provided a circuit shcematic. The schematic does not show the return line for the secondary wire to complete a closed circuit. Nor do schematics show dimensions our layout of the wires.

Here's a good tip to remember. To do circuit analysis we ignore physical layout and size (thank God) and think only of circuit topology. To do field calculations using Maxwell's equations or Faraday's laws, the size, orientation and placement and layout of the wires is the whole ball game and can't be ignored.

Cable B is a signal cable which I do not know how is connected.
However if I only knows cable B runs parallel with cable A for 2200 m and that the rest of the cable B routing is unknown, which means I do not quite know the loop/complete circuit of cable B. But let's assume that after 2200 parallel routing, cable B turns 90 *C away from the cable A (perpendicular to cable A). Will it matter if the unknown routing away from cable A eg. is 1000 m or 5000 m farther away?

Would it be possible to make a assumption for the closed circuit of cable B?
I am not that into how signal cables are connected.

 

[anorlunda]

Cable B is a signal cable which I do not know how is connected.

More important is the power cable. Typically power cables bundle both teed and return together and wrap a jacket around both. In that case, the magnetic field outside the cable is much lower than it would be if the legs were separated. If the power cable was coaxial, the external magnetic field goes to nearly zero.

Take @berkeman 's tip. Use Faraday's law. Map out the size, orientation, and layout of both loops A and B and do the integrations.
Your original analysis was flawed. You assumee that 500A passes through the mutual inductance, that's the kind of error that's likely unless you do it right with Faraday's Law.

 

[berkeman]

Cable B is a signal cable which I do not know how is connected.

Well if it is a "signal cable" for anything faster than DC signals, it will be a pair of wires, not a single conductor with a return wire "somewhere". Can you Upload a picture of the setup?

 

[Tom.G]

Umm... What about the Capacitive coupling?

 

[Babadag]

As it is already said, in order to measure a voltage in the no-load wire you need a closed loop. If the no-loaded wire is not grounded it could be still connected to the ground through the insulation resistance or [parasite] capacitance. A sensible voltmeter could measure the voltage-since the current through the voltmeter will be low.
If the distance is larger an induced voltage could be significant in the ground -as the second part of the loop. In this case the Carson formula it is to be employed and here the reactance between the to wire connected with ground [as a conductor] it is close to k.ln(1/D) and that means indeed the induced voltage will decrease with the distance.

 

[Babadag]

Actually if D increases the reactance will be more negative but in absolute value will increase.