Re: 3 way switches
Ok Al, let's do it.
Actually I'm going to bend a little here.
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I don't think it can be expressed as a "point value".
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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?
The differnece is that the current isn't a field. It's a collection of point charges. The individual values can be known discretely. A field has no independant discrete values. But, this is one of the two points I'll bend on. If you move far enough away it begins to
appear as if the values are combined at a point. But we still know they're not. The reason we're allowed to
pretend the current occupies a near infinatesimal space is because it doesn't effect the measurement of the field outside the conductor and that sure makes it easier. The reality is that you may have to apply skin effect and you know what that means. Think of the gravity of a hollow sphere.
Curvature of space? (space-time). Callin in the big guns, let's see if we can keep Einstien and Maxwell out of this.
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's why I don't think that works. What I think you end up with is a vector sum at a point (used loosely) where there exists a real flux density value. If they don't match (and I haven't checked whether they do) then out with the vector in with the real. But, this is the other point I'm going to bend on.
B=L/A
I'll restate this because there's so many pages.
B = magnetic field (flux density)
L = lines of force (quantity)
A = unit area
This formula demands the lines of force be perpendicular to the plane of the area. We know that the flux lines around the wire are circular. So go figure.
Since you already know how and I'm cutting labor costs on this project I'm interested in seeing Biot-Savart in vector form.
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.
This is how I confirmed what Karl Riley said about inversely proportional. Exept I'm using the formula I posted and u sub o. But those lines that are added together still exist in an area, not a point.
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.
This is where I think you're cramming a square peg. You can arithmeticly change it but you're no longer representing reality. Sometimes that's done for simplification when it doesn't effect the outcome. I think here you're getting the same outcome but complicating it.
Heh! Another idea is to think of the flux in Teslas, not in Webers/ft?
I was gonna tell you that the other day but the math I have has the Teslas disected.
[ November 07, 2004, 03:18 PM: Message edited by: physis ]
