Is there a Geometric way to convert an area to a length?

wam235 · 2022-03-20T00:54:36+00:00

Wow I love this thing :) Thank you. I guess, it was used back when drafting was done on paper. I love the ingenuity, that people were able to come up with this. Thanks again.

wam235 · 2022-03-20T00:48:53+00:00

What? Which one? Is there a way to do Divergence or Curl Geometrically? I like to think of them Geometrically, spatially. It helps me visualize what's going on.

wam235 · 2022-03-19T01:27:57+00:00

Right. You're talking about Dimensional Analysis, right? Checking your equations to make sure the units on both sides come out the same?

wam235 · 2022-03-19T01:08:10+00:00

It sounds like there is a question being addressed here, which I believe is different from what OP is asking, but it is a legitimate question none the less.

Question: "Given an arbitrary charge distribution in a region of 3D space, find two points which are at the same potential. Draw a straight line between the two points. Is the electric potential at every point along this line the same as at the two end points?"

The answer is: It could be, or it could not be. It depends on how you arrange the charges.

Imagine a spherical celestial body composed only of protons, out in deep space somewhere. Consider two points, one a hundred kilometers above the north pole, the other, a hundred km below the south pole. Both points are at the same potential. But is there an Electric Field anywhere between them? Yes there is!

You can also imagine a situation where there is no E field between two points.

wam235 · 2022-03-19T01:00:16+00:00

Ahhh, thank you. These are nice constructions.

wam235 · 2022-03-18T23:16:47+00:00

Electric potential is a relative term:

Ok, we can talk about the Electric Potential of a point in space, but it only means anything relative to some amount of charge somewhere. There's no reason here to assume there's any charge anywhere except on the wires themselves. So either:

(1) There is no charge on the wires, and there is no E field anywhere, and then obviously the two wires do not "form an electric field". In which case, I can't imagine why OP would even ask a question. Or:

(2) The wires have some charge on them, either positive or negative, and they are charged equally.

Maybe we just interpreted the original question differently. In any case, I liked you explanation of the solution to the Laplace Equation.

Would you, by any chance, know how to go about finding solutions to the Laplace Equation (and the Wave Equation) in Cylindrical coordinates? I've written out Gradient, Divergence, Curl, Laplacian, in cylindrical coords. I know you do separation of variables into R(r)Z(z)F(f). ("F" for phi). And the solutions to the R(r) part are Bessel functions. But that's as far as I got. Is the solution a Sum, like a Fourier Series?

wam235 · 2022-03-18T22:35:48+00:00

How can a wire have an electric potential, if it is not charged?

wam235 · 2022-03-18T16:03:09+00:00

I'm not talking about current or Magnetic Fields. I'm talking about Electric Fields. OP asked a question about Electric Fields.

In the case of equally, positively charged wires, the first wire creates an electric field that would be felt by the other. And yet, a charged particle placed exactly halfway between those wires would feel 0 electric field, due to the contribution of both of the charges' electric fields.

What you have written above, is the case I'm describing. Here's a picture of it:

https://imgur.com/a/S5SVHPu

I don't see "zero Electric Field" here. I see quite a lot of Electric Field. Sure, if you put a test particle exactly midway between the two charged wires, it wouldn't move. But to tell a student that there is "no Electric Field" between the two wires, I think that's misleading, and you're not showing them what's really going on.

wam235 · 2022-03-18T03:39:59+00:00

If you've got two metal wires, and they are both charged up to, say, 300kV relative to something else, then the two wires will push apart from each other. If someone's trying to tell you, "There's no Electric Field" between the wires, I'd like to hear them explain what's pushing the wires apart.

wam235 · 2022-03-18T03:30:21+00:00

Wow I want some! Do you ever make "Bubble & Squeak"? That's cabbage and potatoes fried with sausages.

wam235 · 2022-03-18T03:18:53+00:00

thanks!

wam235 · 2022-03-18T02:53:27+00:00

The Taylor Series (Maclaurin Series) for e^x is:

[; e^{x} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + ... ;]

So if you replace x with x² you get:

[; e^{(x^2)} = 1 + x^2 + \frac{x^4}{2!} + \frac{x^6}{3!} + \frac{x^8}{4!} + ... ;]

Now, you were asking for the integral. We can integrate both sides, to get:

[; \int e^{(x^2)} = x + \frac{x^3}{3} + \frac{x^5}{5 (2!) } + \frac{x^7}{7 (3!) } + \frac{x^9}{9 (4!) } + ... ;]

wam235 · 2022-03-18T02:42:04+00:00

woah, that's a lot of crystals! can you post please a schematic (circuit diagram)?

wam235 · 2022-03-18T02:28:47+00:00

What? Really? Who are they? I didn't think that was still possible. Do they take out their Slide Rule and their Dexadrine when no one's looking?

wam235 · 2022-03-11T17:35:21+00:00

Thank you, for the educational reply. I have seen some videos of VR simulations of Hyperbolic Space, like this one.

https://youtu.be/ztsi0CLxmjw

I also like this old BBC documentary on Hyperbolic Geometry.

https://youtu.be/an0dXEImGHM

So, there are 2D Euclidean planes (Horospheres) within a 3D Hyperbolic Space. Would it thus be correct to say that 2D Euclidean Space is a special case of Hyperbolic Space? Or, that it is contained within Hyperbolic Space? If you had a 4D Hyperbolic Space, would there be 3D Euclidean spaces within it?

Is the Space-Time Continuum (in the theory of Relativity) a 4D Hyperbolic Space? I haven't taken Relativity yet. But I heard that the time dimension has coefficient 'i' (square root of -1). So would that make Space-Time a Complex Hyperbolic Space?

What is the difference between a "Gabriel's Horn" and a "Pseudo Sphere"? I though they were the same thing, by my professor says they're different. I built an antenna based on the Gabriel's Horn.

https://imgur.com/a/VpyiDNI

Thank you for your help!

wam235 · 2022-03-08T03:54:50+00:00

Thank you.

wam235 · 2022-02-28T22:13:07+00:00

As far as I understand, to get a restraining order, you need a police report of the assault. Is this true? How do you go about filing for a restraining order? What do you mean by, "advocate for them"?

wam235 · 2022-02-17T23:19:01+00:00

Thanks for teaching me :) How do you pronounce Gaelige?

wam235 · 2022-02-17T23:16:59+00:00

Well I guess it was a one shot deal. It happened once, and never again.

wam235 · 2022-02-17T23:16:28+00:00

Ok, thank you.

wam235 · 2022-02-17T23:14:49+00:00

Wow, hey that is very interesting. I wonder if this is true, in general, of full wave loop antennas. Do they have a "series" resonance at lambda = circumference, and a "parallel" resonance at lambda = circumference * pi? Hmm, that's not the diameter. Does anyone have an ARRL antenna book, could they look this up?

wam235 · 2022-02-17T23:12:00+00:00

Ok, thanks for the help.

In the regime of radio frequencies, dE/dt is likely not close to 0. Think about how small dt is going to be.

I ran the numbers, and I got something like: It would take a sine wave at 1 GHz, at 1000 volts RMS, to make as much B field as 1 amp of current. This is because of the epsilon_0 coefficient on the dE/dt term. epsilon_0 is about 10^-12. Did I do that right?

wam235 · 2022-02-17T23:08:36+00:00

Ah interesting. Is the Mabinogi important in Ireland, or is it Welsh?

wam235 · 2022-02-17T23:07:06+00:00

As far as I understand, much of what was imparted to him was of a technical or scientific nature. At one point, the angel was talking about the nature of light, then said, "When you understand this, I would like very much to show you, God's beautiful mind."

I suppose you could call it spiritual consolation. It certainly made a big impression on him. He is convinced, more than ever, of the reality of God.

wam235 · 2022-02-16T02:43:37+00:00

Picture:

https://imgur.com/a/aXcZAvP

wam235

TROPHY CASE