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#1
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E-Field between 2 parallel wires
MAYBE NOT EXACTLY THE RIGHT GROUP, but..
If I tape 2 insulated, parallel wires to the wall, x cm apart, and then drive a sinewave into them (Vo p-p), how can I calculate the field strength between the 2 wires? For instance, 120KHz, 100V, 5cm apart, what is the field in V/cm between the two wires? Any references or information on how to calculate this would be greatly appreciated. |
#2
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E-Field between 2 parallel wires
Jon Mcleod wrote:
MAYBE NOT EXACTLY THE RIGHT GROUP, but.. If I tape 2 insulated, parallel wires to the wall, x cm apart, and then drive a sinewave into them (Vo p-p), how can I calculate the field strength between the 2 wires? For instance, 120KHz, 100V, 5cm apart, what is the field in V/cm between the two wires? Any references or information on how to calculate this would be greatly appreciated. Is the sine wave applied and the load, if any, connected such that the currents in the two wires are equal and opposite? If so, the problem becomes exactly the same as a single wire suspended above and parallel to an infinite perfect ground plane. In the plane exactly midway between the wires -- the position represented by the perfect ground plane in the simplified model -- the field is zero, since the fields from the two wires are equal and opposite in that plane. If the currents aren't equal and opposite, the problem becomes considerably more complex. By "between the wires", do you mean in the plane of the wires, or some larger region? Are you looking for a closed-form solution, or would a numerical analysis result be adequate? If this is a homework assignment, the professor assigning it should be able to steer you to some suitable references. Roy Lewallen, W7EL |
#3
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E-Field between 2 parallel wires
On Aug 22, 3:23 pm, Roy Lewallen wrote:
Jon Mcleod wrote: MAYBE NOT EXACTLY THE RIGHT GROUP, but.. If I tape 2 insulated, parallel wires to the wall, x cm apart, and then drive a sinewave into them (Vo p-p), how can I calculate the field strength between the 2 wires? For instance, 120KHz, 100V, 5cm apart, what is the field in V/cm between the two wires? Any references or information on how to calculate this would be greatly appreciated. Is the sine wave applied and the load, if any, connected such that the currents in the two wires are equal and opposite? If so, the problem becomes exactly the same as a single wire suspended above and parallel to an infinite perfect ground plane. In the plane exactly midway between the wires -- the position represented by the perfect ground plane in the simplified model -- the field is zero, since the fields from the two wires are equal and opposite in that plane. If the currents aren't equal and opposite, the problem becomes considerably more complex. By "between the wires", do you mean in the plane of the wires, or some larger region? Are you looking for a closed-form solution, or would a numerical analysis result be adequate? If this is a homework assignment, the professor assigning it should be able to steer you to some suitable references. Roy Lewallen, W7EL Hmmm...I don't think that's quite right, Roy. I expect the E field between the wires, in the plane of the wires, to be parallel to the plane, perpendicular to the wires, if there is a potential between the wires and they are straight and parallel. For a wire above ground, the E field must be perpendicular to the ground at the ground (assumed perfect), but it's not zero in general. Cheers, Tom |
#4
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E-Field between 2 parallel wires
Any references or information on how to calculate this would be greatly
appreciated. It's called Classical Electrodynamics. http://www.amazon.com/gp/reader/0471...pt#reader-link "Jon Mcleod" wrote in message m... MAYBE NOT EXACTLY THE RIGHT GROUP, but.. If I tape 2 insulated, parallel wires to the wall, x cm apart, and then drive a sinewave into them (Vo p-p), how can I calculate the field strength between the 2 wires? For instance, 120KHz, 100V, 5cm apart, what is the field in V/cm between the two wires? Any references or information on how to calculate this would be greatly appreciated. |
#5
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E-Field between 2 parallel wires
"Jon Mcleod" wrote in message m... MAYBE NOT EXACTLY THE RIGHT GROUP, but.. If I tape 2 insulated, parallel wires to the wall, x cm apart, and then drive a sinewave into them (Vo p-p), how can I calculate the field strength between the 2 wires? For instance, 120KHz, 100V, 5cm apart, what is the field in V/cm between the two wires? Any references or information on how to calculate this would be greatly appreciated. if you are looking for a closed form solution you will need to investigate some classical electrodynamics methods for wires on a dielectric half plane. There are probably some not so elegant methods to calculate it using the relative dielectric constants of the air on one side and the wall material on the other. The field will of course be different in the wall material than in the air. as a first approximation you can take an average of them and use that to estimate the field as if the conductors were embedded in an infinite block of dielectric material, that is probably a simpler problem. there are programs that will do finite element analysis and come up with numerical solutions, that is probably simpler in most cases than the raw field equations. For a relatively low frequency like 120khz and those low voltages you can bound the problem by assuming 2 wires in air... 100v/5cm=20v/cm half way between the wires... with a material on one side it will usually have a lower field than in the air by approximately the ratio of the relative dielectric constants. For wood the constant depends a lot on moisture content, from a low of maybe 5 up to 100 for saturated wood. The higher the dielectric constant the lower the field in the material, as a first approximation with a constant of 5 you could guess that 80% of the field was in the air and 20% in the wall... and of course the farther from the wires the lower the field... so from a max of maybe 20v/cm between the wires the field will decrease as you move away from the wall in air, and decrease about 5x faster as you move into the wall. the hard part is close to the wires, there it depends on the diameter of the wire, the smaller the diameter the higher the field, to get those numbers you need one of the other methods above. |
#6
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E-Field between 2 parallel wires
K7ITM wrote:
On Aug 22, 3:23 pm, Roy Lewallen wrote: Is the sine wave applied and the load, if any, connected such that the currents in the two wires are equal and opposite? If so, the problem becomes exactly the same as a single wire suspended above and parallel to an infinite perfect ground plane. In the plane exactly midway between the wires -- the position represented by the perfect ground plane in the simplified model -- the field is zero, since the fields from the two wires are equal and opposite in that plane. If the currents aren't equal and opposite, the problem becomes considerably more complex. . . . Roy Lewallen, W7EL Hmmm...I don't think that's quite right, Roy. I expect the E field between the wires, in the plane of the wires, to be parallel to the plane, perpendicular to the wires, if there is a potential between the wires and they are straight and parallel. For a wire above ground, the E field must be perpendicular to the ground at the ground (assumed perfect), but it's not zero in general. Cheers, Tom Tom is completely right -- as always. The problem is, as I said, the same as a single wire suspended above a perfect conducting plane. The E field is perpendicular to the conducting plane (that is, in the plane containing the wires as Tom said) and not zero as I incorrectly said. Thanks for the correction, Tom, and my apology to all for the error. Roy Lewallen, W7EL |
#7
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E-Field between 2 parallel wires
On Aug 22, 2:49 pm, Jon Mcleod wrote:
MAYBE NOT EXACTLY THE RIGHT GROUP, but.. If I tape 2 insulated, parallel wires to the wall, x cm apart, and then drive a sinewave into them (Vo p-p), how can I calculate the field strength between the 2 wires? For instance, 120KHz, 100V, 5cm apart, what is the field in V/cm between the two wires? Any references or information on how to calculate this would be greatly appreciated. I'm tempted to make some statements that I can't quite prove without doing a bit of math, but I'll refrain... But I will recommend the program ATLC ("Arbitrary Transmission Line Calculator"), which does calculate the electric and magnetic fields numerically. Except for changes in the current distribution because of changes in skin depth versus frequency and changes the dielectric versus frequency, I don't think there's any effect of frequency on the fields distribution for a TEM-type line, where the current in the two conductors is equal amplitude but opposite direction and the line is in a uniform dielectric. Taping it to a wall will make is "quasi-TEM" but you can expect the electric field direction to be very close to being in a plane perpendicular to the axis of the wires. Cheers, Tom |
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