3 way switches

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Re: 3 way switches

Jap,

I'll bet that the two threewires that come to that fourway switch you openned are mounted close together along their length (at least based on what I understand you to have written).

Even though the currents are in two different cables, it sounds like they are relatively close together. . .in the order of parts of a foot. When one backs up tens of feet from them, the net measurable magnetic field is effectively zero.
 
Re: 3 way switches

Keep It Simple Stupid
Click to expand...
So much for my last approach to magnetic fields.

Edit: cool link Jim

[ November 05, 2004, 05:43 PM: Message edited by: physis ]
 
Re: 3 way switches

I knew all alone I would find a new name for this switch and get the insult away from Tennessee.

I introduce the KISS three way :)
 
Re: 3 way switches

Hello Ronald, in your version EMF is eliminated. ;)

Roger
 
Re: 3 way switches

Sam,

Looking at the copy of the formula you posted for Biot-Savart,

The "element" is a differential amount of the current flowing in a "straight, fine line."

Integrating the differential equation you posted for a straight, fine line of current that goes to infinity in both directions reduces the formula to:

B = a(0.0000002)(?)(I)?r

Where:</font>
  • <font size="2" face="Verdana, Helvetica, sans-serif">B = The vector magnetic flux density at a "point"</font>
  • <font size="2" face="Verdana, Helvetica, sans-serif">a = a unit vector in the direction of the field at the "point"</font>
  • <font size="2" face="Verdana, Helvetica, sans-serif">r = the radial distance from the line of current (at a right angle to it) to the "point." This is the shortest or most direct distance from the "point" to the line of current.</font>
  • <font size="2" face="Verdana, Helvetica, sans-serif">? = the permeability of the space along the distance r</font>
  • <font size="2" face="Verdana, Helvetica, sans-serif">I = current (the integral of the differential "element")</font>
<font size="2" face="Verdana, Helvetica, sans-serif">
 
Re: 3 way switches

Hello Roger

Are you sure Bennie use to kid about using the barbed wire fence as the grounded conductor. :D

You know since we can't find anyone that can really put a name on the Chicago threeway switch or what ever.We ouhgt to Name it the Bennie Palmer Threeway at least on this forum.

[ November 05, 2004, 09:12 PM: Message edited by: ronaldrc ]
 
Re: 3 way switches

Thats right Physis

And in Tn. we just have to use one wire and I bet 10 wire nuts you all can't do it with just one wire even if you use the barbed wire fence. :)
 
Re: 3 way switches

Al, Try this:

B=(uI)/(2Pir)

B = magnetic field (flux density)
u = permiability constant
Pi = 3.1415926
r = distance from wire
I = current

This confirms Karl Riley's assertion that the field is deminished directly to the distance. Go Karl. :cool: I went to a lot of trouble to prove myself wrong.

You're right about B being the flux density. But I don't think it can be expressed as a "point value".

It's too bad we don't have Greek letters. I have to invent variables again.

B=L/A

B = flux density
L = lines of force (quantity)
A = area

Magnetic flux density is the number of lines of force per unit area. I don't know of a way to convert that to a vector unless you're after a coordinate on the plane of that area and I don't know what meaning that would have.

Edit: Ronald, I think I can do it with only the barbed wire fence, no wire nuts. But there has to be some illegal current being drawn off the fence, maybe to power the still.

[ November 06, 2004, 12:48 AM: Message edited by: physis ]
 
Re: 3 way switches

Hey Sam,

It's been quite a while since I've gone through this level of math. Please pardon my obvious rust.

The magnetic flux density at an area (being a number representing so many "lines of force") is also lines of force that are oriented in a direction. It is the direction that allows B to become the vector B.

Think of a fine, straight line of current going from left to right. Lets have this line represented on a sheet of paper in front of us. The current has a magnitude and direction.

If I look at a point on the paper, a point below the line of current, the right hand rule tells me that the magnetic field is going into the paper. Think of reaching into the paper at the line of current, grabbing the line, wrapping the fingers around the line with the thumb extended, like the hitchhiker's thumb out, thumb pointing in the direction that the current is heading. The fingers wrap around the current in the direction of the cylindrical magnetic field, pointing from north to south. . .except this is a cylindrical magnetic field without a beginning or end in the sense of the north or south poles of a physical magnet.

At a distance r from the fine, straight line of current, we imagine a cylinder, like the wall of a can, that is the field. For mathematical purposes of simplification, the fine, straight line of current is allowed to approach zero height and zero depth with infinite length, coming from the left, going to the right, and the thickness of the wall of the can is allowed approach zero.

The formula you've just posted is the result of the integration of the differential equation you posted earlier.

Keeping the direction of the flux, especially mathematically, will allow us to go from this static DC image of the current and field to the sinusoidally varying AC model. That's where vector analysis pays off.

One side note: ?, the permeability constant in your formula above, is actually ? sub zero, or the magnetic permeability of free space (which is a constant) multiplied by ? sub r (which is specified at the time of calculation), the permeability of whatever is along the radial distance r between the current and the point that B or B is being calculated for.

(? sub zero) ? 2 Pi = 2 x 10 to the minus 7th = .0000002

Maybe someone else can add a bit to this. . .like I said, I'm rusty.
 
Re: 3 way switches

Hi again Al,

The magnetic flux density at an area (being a number representing so many "lines of force") is also lines of force that are oriented in a direction. It is the direction that allows B to become the vector B.
Click to expand...
The only problem is that flux density is a measure of the number of flux lines per unit area perpendicular to the lines. The only angle allowed between the lines and the plane of the area is 90 deg. Otherwise you're not measuring flux density. :)

I know the permiability constant is u sub o. You just can't type that here. ;)
 
Re: 3 way switches

Hey Sam,

Yeah, I haven't found a trick for subscripts, either.
I don't think it can be expressed as a "point value".
Click to expand...
Mathematically it can. It's analogous to the current we're talking about that is inducing the field. The current, theoretically, is in a conductor with no height or depth, yet is infinitely long and straight. Physically this makes no sense. . .super conductor technology not withstanding. . .and what about the curvature of space?

Vector calculus allows the calculation of B at any point on the circular path of the flux. The vector that is tangent to the circular path points in the direction of the flux, and the magnitude of the vector corresponds to the flux density at that point. The Biot-Savart law is a vector formula.

Here, think of it this way, as we change the radial distance from the conductor to where we are calculating the flux density, we find the flux density changes (let I and ? sub r remain constant). If I try to look at a unit crossection area of the flux, all the points that are at different r need to calculated and added together.

That's a messy and long piece of arithmetic.

If I write a differential equation representing the change of B with respect to the change of r and then integrate it for a specific point, I can then get a result that represents the flux at a point r away from I as if the flux were uniform across an area.


Heh! :) Another idea is to think of the flux in Teslas, not in Webers/ft?
 
Re: 3 way switches

Al and Physis, you're educating me. I have an aversion to complex math, so I have always relied on actual measurements. But it's nice to hear the math discussed.

With a single-axis or tri-axial gaussmeter it is easy to measure the field drop-off as you come away from various sources.

What I discovered by graphing my results was that coming away from a single conductor (Al, not necessarily between the conductors, as that is a loop and the field weakens more slowly), the field weakens directly with distance. This surprised me since the standard quote from engineers is with the square of the distance.

Then I measured from power lines and found the square of the distance. The field is easily measurable because the phases are spaced apart.

Then I measured from coil sources such as small transformers. The field weakens with the cube of the distance! This was all pure discovery for me, since I had not read this anywhere. But the results are clear and make beautiful graphs. If the coil is large like a utility Tfrmer, it weakens with the square for a few feet, then with the cube, since as you get farther away it acts more like a point source.

The field from appliances is almost always a coil source, which is why the fields weaken so fast, and why appliances have not been found to be a major source of exposure. Computer monitors used to be until the Swedish established a mG standard and all manufacturers adopted it in order to sell in Europe. Since the field was from the coil around the neck, they just added a cheap counter coil to cancel the field.

Of course, the field is a vector so you have to always line up your single-axis sensor with the field. How do you know you're lining up? Simply because the measurement peaks. A three-axis meter will give you the same results, since it measures partials of the vector and calculates the vector sum.

It's more fun to do hands on stuff than try to find the formulas, I find.

Karl
 
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