Anyone here know electromagnetism really well?

[Bowman]

I once had an MR so Electromagnetism got to know me very well.
Sadly I am only familiar with it... she's lucky I remember her name.

But I do know that most of our technology would not exist without it so I have a great deal of respect for it.

 

[kenstarr]

This is from yesterday at work. Some Mysterious Electrical Stuff going on. It's the exterior of a 5000 amp transfer switch. Was 150 degrees fahrenheat earlier in the day. Strange parts of the cabinet are hot. Inductive heating???

 

[OverTheTop]

It isn't a shiny reflection of something else, is it. That has fooled other people here before. Also I assume you have your emissivity setting correct for what you are looking at? Of course, it could be real too .

 

[John Kemker]

First, you have to consider what "thin" means. The equations given the books are perfect if and only is the wire is truly one dimensional. "Thin" means that the cross-sectional dimensions of the wire are much smaller than the distance between the wire's surface and the point in space at which you want to know the field. If your point of interest is at least, oh, let's say, four diameters away then the deviations from the equations are very small. If you're ten diameters away then the deviations are trivial. (The magnitude of such deviations will fall off approximately with the cube of distance, just like dipole fields and tidal forces.) Keeping that in mind...

If the wire is perfectly round, and the point where you want to know the field is outside of it, then the equations are exactly correct with the distance being measured from the center line of the wire.


Even at DC, it's not quite as simple as Mr. Funk stated above, because even at DC the current density is not uniform throughout the wire. So you can add up the fields created by an infinite number of differential segments of the wire, but only if you first compute the current density field within the wire. Which is a staggeringly ugly thing to have to do. The result will be as stated earlier, something that approximates the shape of the wire but with all the corners rounded. The further away you get, the more the corners round out, until they overlap and the straight sides (which were never completely straight to start with) disappear. Then as you move further out, and the former corners want to all become one, you've got the same circular field that you would have if the wire were round, barring trivial deviations.
As Mr. Funk stated, there is no magnetic field created inside the pipe. Subsequent statements that yes, there is a field inside the conductor, apply to solid conductors, magnetic fields inside the metal, the rise of skin effect, etc. But inside a hollow conductor, i.e. inside a pipe, no.

What if the wire is neither thin nor round? Well, we're still looking at a matter of scale. If the wire is a square 1 mm on a side then the field will just the same as for a round wire, provided you're at least a centimeter away. If the square is an inch on a side, get ten inches away.

The interesting cases which you didn't mention are where the third of those words is not true.
1. Not thin? No problem.
2. Not round? No problem.
3. Not straight? Now you're talking!

You know the answer when the wire is straight: a "cylindrical field" with the wire as it's axis.

And you know the answer when the current flows evenly around the surface of a cylinder: straight parallel field lines along the center of the cylinder. That's the idealized version of a coil if said coil has infinite length, and if not then you get a dipole field with lines diverging/converging at the ends of the coil.

But if the current is in a bendy wire, then there'll be a hot time in the old town tonight. In a single bend it seems simple on its face: the field will resemble that for a straight wire, but becoming intensified along the inside of the bend and weakened along the outside, right? Just like the coils of a slinky, which are uniformly spaced if the slinky is pulled straight, but bunch up or spread out when the slinky bends around a corner. Well, I think that's right, but I won't swear to it. And even if that is right, just go trying to write the equations for it. Then reverse the bend to make an S. And let another, separate wire cross nearby, taking its own curvy path. This is why PCB design for high frequency applications is a black art practiced exclusively by members of a secret society. Those guys think antenna designers are just adorable.

No.

The frequency of oscillations of the magnetic field is the same as that of the current that induces it. There are no inner and outer frequencies. Well, not exactly. I'll get back to that.

The skin effect is an interaction between the current density field and the magnetic field that said current creates. The magnetic field pushes the current out toward the surface of the wire, and this effect is greater at greater frequency. When the frequency is high enough, the current is flowing almost exclusively in a thin layer just below the metal's surface, and the effect is therefore called "skin effect". The thinner the skin, the less of the metal the current is using, so the more resistance the current sees, as if it were flowing in a much smaller wire. Wires for high frequency signals are many stranded so that the diameter of each strand can be less than the skin depth, and thus all the metal is used, and the effective resistance is a lot lower.

Getting back to "there are no inner and outer frequencies", If I understood correctly what you meant then I stand by it. But signals that are not simple sine waves have a spectrum to them. The skin effect affects the higher frequency components of the signal more than it does the lower frequencies, so the lower frequencies use the inner portion of the metal more. So the lower frequency components of the signal see lower resistance than the higher frequency components. So the signal is distorted as it travels down the wire.

The same stranding method mentioned above helps with this. But with PCB traces you can't do that. So what I said above about high frequency PCB layout and the people who do it? Yeah.

My head just exploded.

Thanks for the explanation, Joe!

 

[SDramstad]

Ever since I got my shot I have been attracted to magnets…..

 

[jqavins]

Lots of misinformation in this thread.

For DC current in a solid conductor of non-magnetic material, there's a (nearly) linearly increasing magnetic field INSIDE the conductor, with 0 at the center.

It's only inside a pipe that the statement was that there is no field, not for inside a solid conductor. Indeed, in a solid conductor with uniform current density^*, the field grows as you say. In the hollow space in the middle of a tubular conductor, there's no field. For any given closed path, as I'm sure you know, the integral of the field around the path is proportional the the current penetrating the surface it surrounds. The current through the surface increases with the area, so the square of the radius, and the path length increases linearly, so the field strength, as you say, grows linearly. But for the tubular conductor, for any path in the hollow space, there is no current encircled, so there is no field.

Then the magnetic field decreases exponentially outside the conductor.

Inversely, not exponentially. The encircled current ceases growing once the radius exceeds that of the conductor, and the path length continues to grow linearly, so the field drops off inversely.

* But in reality the current density isn't uniform, because the skin effect, or Hall effect of you prefer, does decrease the current density at the conductor's center.

For AC, it's similar to the above except the magnetic field inside the conductor is constantly changing. But, it's peak magnitude increases exponentially from 0 at the center to maximum at the surface (instead of linearly with DC).

Now here, I admit, I am less sure of many things. One thing I am sure of, however, is that nothing grows exponentially from zero. That's not how exponentials work. Perhaps it grows quadratically, or some such?

2) A solid cylinder has a circular field wrapped around it's belly. But if you hollow it out into a pipe, the field orientation rotates 90° and runs end-to-end. (my struggle became very real right about here lol)

Ooo, that sounds like I may have led you astray. But I've typed all my thumbs can stand for a little while, so I'll have to come back to this point.

 

[jsdemar]

It's only inside a pipe that the statement was that there is no field, not for inside a solid conductor. Indeed, in a solid conductor with uniform current density^*, the field grows as you say. In the hollow space in the middle of a tubular conductor, there's no field. For any given closed path, as I'm sure you know, the integral of the field around the path is proportional the the current penetrating the surface it surrounds. The current through the surface increases with the area, so the square of the radius, and the path length increases linearly, so the field strength, as you say, grows linearly. But for the tubular conductor, for any path in the hollow space, there is no current encircled, so there is no field.
Inversely, not exponentially. The encircled current ceases growing once the radius exceeds that of the conductor, and the path length continues to grow linearly, so the field drops off inversely.

* But in reality the current density isn't uniform, because the skin effect, or Hall effect of you prefer, does decrease the current density at the conductor's center.

Now here, I admit, I am less sure of many things. One thing I am sure of, however, is that nothing grows exponentially from zero. That's not how exponentials work. Perhaps it grows quadratically, or some such?

"Decrease exponentially" is anything that decays in a non-linear fashion. "Increase exponentially" is anything grows in a non-linear fashion. Quadratically is exponential of second order.

A hollow conductor, in general, has no internal field in it's empty core if it's theoretically perfect and uniform. However, a special case is a resonant cavity, such as waveguide. Propagation of EM energy doesn't require a conductor. Even a conductive boundary is not necessary.

 

[brockrwood]

I'm scratching my head on a couple of 'what ifs' regarding the shape of the magnetic field that gets set up around a current-carrying wire.

It's well known a thin round wire throws a circular field outside itself when carrying current. Right hand rule and all. But my Googling always shows it worded exactly that way: 'thin round wire'. What if you played with each of the words in turn? What shape does the magnetic field have then?

What happens if the wire isn't thin? What if it's say, inches in diameter?

What happens if the wire isn't round? What if the wire is triangular in cross section? Or square?

What happens if the wire isn't even a wire, but is instead a pipe (hollow)? Is there a field both inside and outside?

Thanks, I'm really curious about this. (is there software where I could play with stuff like this?)

Calling James Clerk Maxwell. Can your hear us?

 

[Sandy H.]

I happen to work around some 'relatively' high current DC (technically 6 or 12 pulse rectified AC->DC) power supplies. The small one is 5000A, the big one is 23kA and there are a few between.

Based on the process, at times we can stick Cresent wrenches to the enclosure when current is high and they stick, which is kind of cool.

During a maintenance shut-down, we also found tons (not weight, just bunches of them) of iron filings stuck to the bottom of the walkways, looked like fur and wasn't easy to clean up. No clue where it all came from, as iron/steel isn't typically in the area.

Pretty sure large DC currents make both temporary magnetic fields and can magnetize ferrous materials in the region. No clue how to simulate it, though.

Sandy.

 

[SecondRow]

Calling James Clerk Maxwell. Can your hear us?

 

[jsdemar]

View attachment 478439

The vector notation equations are the work of Oliver Heaviside. He reduced Maxwell's 20+ equation into the 4 commonly used today. Among other things, he developed transmission line theory, AC circuit theory, relativistic effects preceding Einstein and Feynman, and step response of systems. A deaf recluse with little formal education. Here's a good biography:
https://www.amazon.com/Oliver-Heaviside-Electrical-Genius-Victorian/dp/0801869099

 

[brockrwood]

I'm scratching my head on a couple of 'what ifs' regarding the shape of the magnetic field that gets set up around a current-carrying wire.

It's well known a thin round wire throws a circular field outside itself when carrying current. Right hand rule and all. But my Googling always shows it worded exactly that way: 'thin round wire'. What if you played with each of the words in turn? What shape does the magnetic field have then?

What happens if the wire isn't thin? What if it's say, inches in diameter?

What happens if the wire isn't round? What if the wire is triangular in cross section? Or square?

What happens if the wire isn't even a wire, but is instead a pipe (hollow)? Is there a field both inside and outside?

Thanks, I'm really curious about this. (is there software where I could play with stuff like this?)

There must be a website with a table that shows the magnetic field strength based on the current and the kind/thickness/type of wire carrying it.

 

[brockrwood]

How about this calculator?

https://www.eeweb.com/tools/wire-self-inductance-calculator/

 

[Grog6]

The overheated cabinet could be heating from skin effect at that current level, but 60Hz would be rare to manifest it.

 

[jqavins]

"Decrease exponentially" is anything that decays in a non-linear fashion. "Increase exponentially" is anything grows in a non-linear fashion. Quadratically is exponential of second order.

I'm sorry, but that is just absolutely dead wrong. Exponential growth (or decay) is the growth or decay of some value with respect to some other value - most often time but in this case distance - whose rate of growth (or decline) is directly proportional to it's value. It is characterized mathematically as Y=Y₀e^ax, where a is less than zero for decay. An exponentially growing or decaying value can never be zero, as that would cause its rate of change to be zero.

Quadratic growth is characterized by y=Ax²+Bx+C, often just y=Ax². This is not an exponential of second order, but rather it is a polynomial of second order.

Exponential growth is often very rapid, even explosively so. This had led to the word being used in popular media in recent years, incorrectly, to refer to any very rapid growth. While polynomial growth (quadratic or of higher order) can, indeed, be very rapid, it not exponential.

Regarding resonant cavities, that's an entirely different subject. EM waves introduced into the cavity, if they are of appropriate wavelength, will persist, and thus there are magnetic fields as part of said waves. Current carried on the skin of such a cavity, however, do not induce magnetic fields on the inside (unless some nonlinear effects are at play, which they will not be for DC).

 

[cvanc]

2) A solid cylinder has a circular field wrapped around it's belly. But if you hollow it out into a pipe, the field orientation rotates 90° and runs end-to-end. (my struggle became very real right about here lol)

Ooo, that sounds like I may have led you astray. But I've typed all my thumbs can stand for a little while, so I'll have to come back to this point.

Understood

So what is the correct answer here?

When you hollow a solid wire out into a pipe does the magnetic field flip 90° and start to run end to end? Or does it stay wrapped around the pipe's waistline, so to speak, just like the solid wire? Thanks!

 

[jqavins]

Understood

So what is the correct answer here?

When you hollow a solid wire out into a pipe does the magnetic field flip 90° and start to run end to end? Or does it stay wrapped around the pipe's waistline, so to speak, just like the solid wire? Thanks!

I stays wrapped around the wire. What I was trying to describe, and did in a regrettably misleading job, is what you get if the current is going around in rings; then the magnetic field is along the axis of the rings. The lines of current and the magnetic field lines have switched places. That's what you get in a coil of wire, if there's no solid core to confuse matters.

There are other situations wherein electric and magnetic phenomena are not only related, but symmetrical. It's all there in Maxwell.

 

[jsdemar]

I'm sorry, but that is just absolutely dead wrong. Exponential growth (or decay) is the growth or decay of some value with respect to some other value - most often time but in this case distance - whose rate of growth (or decline) is directly proportional to it's value. It is characterized mathematically as Y=Y₀e^ax, where a is less than zero for decay. An exponentially growing or decaying value can never be zero, as that would cause its rate of change to be zero.

Quadratic growth is characterized by y=Ax²+Bx+C, often just y=Ax². This is not an exponential of second order, but rather it is a polynomial of second order.

Exponential growth is often very rapid, even explosively so. This had led to the word being used in popular media in recent years, incorrectly, to refer to any very rapid growth. While polynomial growth (quadratic or of higher order) can, indeed, be very rapid, it not exponential.

Regarding resonant cavities, that's an entirely different subject. EM waves introduced into the cavity, if they are of appropriate wavelength, will persist, and thus there are magnetic fields as part of said waves. Current carried on the skin of such a cavity, however, do not induce magnetic fields on the inside (unless some nonlinear effects are at play, which they will not be for DC).

Your explanation is not mathematically correct. It's just your specific use of the words as you understand them. No need to sidetrack the discussion with pedantics.

My post describing the distribution of magnetic fields (DC and AC) inside and outside conductors (non-magnetic material and magnetic material) is correct. Diagrams would help but I'm too lazy.

Resonant cavities are a special case, not "an entirely different subject".

Also, there is no such thing as DC or steady-state AC in a real system (only in beginning textbooks)... the real system has to be turned on which causes initial transients. There's also relaxation time for the fields inside of conductors and cores which produce extremely short non-uniform field distributions, even inside the hollow cavity.

Take a look at this MIT lecture on relaxation and skin effect. Be careful, it uses your banned phrase "exponential decay". ;-)

 

[kenstarr]

Regarding the very hot electrical cabinet I posted about and didn't mention was one thing the original electricians did... They ran all of A phase in the same pipe, same with B, C, and neutral. I think they stuck a ground in the same pipe as the neutral but I'm not sure.... Great work fellas

 

[cvanc]

Regarding the very hot electrical cabinet I posted about and didn't mention was one thing the original electricians did... They ran all of A phase in the same pipe, same with B, C, and neutral. I think they stuck a ground in the same pipe as the neutral but I'm not sure.... Great work fellas

You are NOT supposed to run 3Φ in separate pipes - and the reason I was always given is "it makes an unintended transformer with the metal pipes and everything gets real hot". Whereas all the phases (incl. neutral) in one pipe makes all the fields kind of cancel out.

 

[OverTheTop]

I agree that the fields should all cancel if run in the same conduit. I was going to say that if the phases were unbalanced all bets would be off, but on considering that situation, assuming the current return path (neutral or other phases) is in there as well it should still hold.

There could be some problems with high-frequency harmonics introduced by high-power loads that might make for some interesting foibles. I have seen that cause some issues with neutral currents in a large building in Canberra where one of our spectrometers was. They had decent harmonics up to about 20kHz.

 

[jqavins]

I agree that the fields should all cancel if run in the same conduit. I was going to say that if the phases were unbalanced all bets would be off, but on considering that situation, assuming the current return path (neutral or other phases) is in there as well it should still hold.

On top of which, even if the net current were somewhat out of whack, somehow, "imbalanced" generally means "imperfectly balanced", where what was done is the maximum possible imbalance. So are all bets off? No, you can still safely be it's a lot better that one phase per conduit.

 

[cvanc]

I'm not one, but I think "all phases in a single pipe" is Licensed Electrician 101, is it not?

 

[kenstarr]

Yes all phases should run together ABC, neutral if present, ground... Same pipe for parallel applications. The code gives some exceptions. I'm not sure why or when you would want to invoke those exceptions however.

 

[Grog6]

I designed a power supply for a data AQ system once that required 120A @ 3.3V. Run 30 feetacross to a cabinet mounted 10ft off the floor.I remember thinking" damn that's 260mcm cable"!



Oh no; 350mcm with a heavy shield!!

This went to the dumpster after that project was over. That's a 50 cent piece.

 

[jqavins]

That's a lot of copper to throw away.

 

[DES]

I designed a power supply for a data AQ system once that required 120A @ 3.3V. Run 30 feetacross to a cabinet mounted 10ft off the floor.I remember thinking" damn that's 260mcm cable"!

Oh no; 350mcm with a heavy shield!!

This went to the dumpster after that project was over. That's a 50 cent piece.

I once had a Russian electrician show me the "proper" way to pencil down 500 mcm conductors with a pocket knife so the wire would fit under the lugs of a QOB molded case breaker (maybe big enough for 1/0). He insisted he did it all the time, was rather surprised when 1) Nope, not gonna fly and 2) This cable is supposed to land on the transfer switch on the other side of the room... Everything was 20 feet too short and had to be repulled.

 

[OverTheTop]

I designed a power supply for a data AQ system once that required 120A @ 3.3V. Run 30 feetacross to a cabinet mounted 10ft off the floor.I remember thinking" damn that's 260mcm cable"!



Oh no; 350mcm with a heavy shield!!

This went to the dumpster after that project was over. That's a 50 cent piece.

View attachment 478672

That cable would have made good jump-start cables for your car.

 

[JoePfeiffer]

Your explanation is not mathematically correct. It's just your specific use of the words as you understand them. No need to sidetrack the discussion with pedantics.
<snip>
Take a look at this MIT lecture on relaxation and skin effect. Be careful, it uses your banned phrase "exponential decay". ;-)

All the same, his correction regarding polynomial and exponential functions is mathematically correct (pedantic? Pedantic is what I did for a living for decades!). In the lecture you posted a link to, the functions being described as exponential really are exponential, not polynomial.

 

[jsdemar]

All the same, his correction regarding polynomial and exponential functions is mathematically correct (pedantic? Pedantic is what I did for a living for decades!). In the lecture you posted a link to, the functions being described as exponential really are exponential, not polynomial.

He was not mathematically correct in the context of explaining the fields within and outside a conductor. I suppose one could make polynomial approximations of transformed field equations, but they won't be real algebraic polynomials.
As you already (sadly) know, I can be just as ruthlessly pedantic as most retired professors. ;-)