Linden Prize! Exercise your mind.

[Aelus]

Show work, and final equation. First person to post the correct equation earns L$2000.

Hint:

http://www.wikipedia.org/

http://web.mit.edu/sahughes/www/8.022/index.html

[Gunau Sodwind]

purely masterbatory my friend.

[Scientific Waffle]

:O oh fun. Looks like it'll need some calc, I'll take a shot at it ^_^

[ribena Homewood]

Brb e-mailing Stephen Hawking, he'd do this in two seconds. That $2000 is mine.

Edited April 20, 2009 by ribena Homewood

[Scientific Waffle]

I don't expect to get it first time around, but here's my first shot... small numbers will be written as x(a) where a is the subscript.

large coil = coil 1

small coil = coil 2

1: B = μ₀ * n₁ * I₁

1: B = μ₀ * n₁ * I₀ * sin(ω * t)

1: dB/dt = μ₀ * n₁ * dI/dt

1: I = I₀ * sin(w * t)

1: dI/dt = I₀ * ω * cos(ω * t)

1: dB/dt = μ₀ * n₁ * I₀ * ω * cos(ω * t)

dB/dt is the changing magnetic field through the center of both loops. Because the small loop is very small relative to the large loop (and due to the concentration of the magnetic vectors of low deviation (from the central axis of the wires) that are resultant from the large coil), we can use this dB/dt for the magnetic field going through the entire area of the small loop as a useful approximation.

2: Φ = A₂ * B₂

2: dΦ/dt = A₂ * dB/dt

2: dΦ/dt = A₂ * μ₀ * n₁ * I₀ * ω * cos(ω * t)

2: ε_ind = -N * dΦ/dt

2: ε_ind = -N₂ * A₂ * μ₀ * n₁ * I₀ * ω * cos(ω * t)

2: A = π * r²

2: A₂ = π * (r₂)²

Our solution is (within the approximation previously stated) ...

ε_ind = -N₂ * π * (r₂)² * μ₀ * n₁ * I₀ * ω * cos(ω * t)

----------------------------------------------------------------------------

You may have a different equation if you did not use the same approximation route I chose, or if you did not ignore relativistic effects. Or I could be completely wrong :P

Also note, π is pi.

Edited April 21, 2009 by Intus Infinity
Random math formatting.

[Aelus]

Scientific Waffle has proven to be a delicious winner!

The approach was perfect--yes, it was an approximation.

Since the answer calls for a magnitude scalar, we can make the assumption that you planned on dropping the negative.

Again, perfect! I'll contact you in game.

[Gunau Sodwind]

4

[Cygna]

Good game, Waffle. Going to format some of your math :o

In the reply to topic posting view, you can see next to "b" "i" and "u" the button with two a's (a small a and a capital A). In there you can ^superscript and _subscript.

[Agares Tretiak]

Let's try something from the humanities, in the future. and none of this namby-pamby grade school reports, but hard core analysis.

[Aelus]

namby-pamby grade school reports

Yeah! Because you know, anyone can easily understand electromagnetism and the Maxwell equations. Analyzing things is so hard!

[Trevor Russell]

Yeah! Because you know, anyone can easily understand electromagnetism and the Maxwell equations. Analyzing things is so hard!

Actually, I did this stuff senior year of highschool. Also, just looking at the problem briefly, shouldn't a numerical answer be the final? I call shenanigans.

[Aelus]

Actually, I did this stuff senior year of highschool. Also, just looking at the problem briefly, shouldn't a numerical answer be the final? I call shenanigans.

High school? Oh wow, how impressive! What's the name of the school? Also, the final equation is all that is necessary--a scalar value doesn't show much.

Since you're a veteran at this, how about an easy one for you to solve:

[Agares Tretiak]

I think you misunderstood. I meant if you do something from the humanities, it's not rote memory style crap, but actually analysis and synthesis. Sheesh. ANd trust me, actually analysis of things like historical data is apparently a lot harder for people to do than they realize.

[RazorFox]

I pose the following philosophical dillema.

If a tree falls in the woods and no one is around to hear it, does anyone care?

[Agares Tretiak]

Only if you count forest animals as "someone". If yes, then they probably care for a little while. If no, then really, only reaaaaally bored people would care.

[Scientific Waffle]

Actually, I did this stuff senior year of highschool. Also, just looking at the problem briefly, shouldn't a numerical answer be the final? I call shenanigans.

He asked for the equation in the original post, not a numerical answer.

And Agares, physics is not plug and chug memorization, it's analyzing how the universe works. You can't just memorize equations to solve something like this, there's a lot of analysis and interpretation for physics like this. I analyzed what physical phenomena the described setup produced, and then synthesized multiple equations together based upon an approximation I had to come up with on my own. There's a difference between rote math problems and physics, Agares.

[Cygna]

He asked for the equation in the original post, not a numerical answer.

And Agares, physics is not plug and chug memorization, it's analyzing how the universe works. You can't just memorize equations to solve something like this, there's a lot of analysis and interpretation for physics like this. I analyzed what physical phenomena the described setup produced, and then synthesized multiple equations together based upon an approximation I had to come up with on my own. There's a difference between rote math problems and physics, Agares.

Agreed.

[Aelus]

And Agares, physics is not plug and chug memorization, it's analyzing how the universe works. You can't just memorize equations to solve something like this, there's a lot of analysis and interpretation for physics like this. I analyzed what physical phenomena the described setup produced, and then synthesized multiple equations together based upon an approximation I had to come up with on my own. There's a difference between rote math problems and physics, Agares.

Very well said.

[Agares Tretiak]

I think, once again, you didn't read what I was saying.

I was talking about the humanities. Art, philosophy, history, sociology, etc. Please read subsequent posts that clarify the issue. -_-

Since you haven't, I'll provide a longer, more complex answer:

I was talking about analysis of historical and sociological data, as opposed to boring old "What important event occurred in 1845 that yadda yadda yadda and changes the yadda yadda" Which is basicly a rote memory boring old report. God damn, people. You seemed to assume I was attacking physics equations.

Examine contextual clues in the sentence! D:<

[Tiridates Mikadze]

Humanity is a universe all it's own, to be honest, and no amount of physics equations can ultimately define it.

And it is imminently present in all our interactions. Just like Physics.

[Scientific Waffle]

Humanity is a universe all it's own, to be honest, and no amount of physics equations can ultimately define it.

And it is imminently present in all our interactions. Just like Physics.

I'd tend to disagree; the need for models of human nature are due to the limitations of men rather than physics in my opinion. The reason sociology and human interaction is not described through physics is due to the staggeringly complex nature of it. All of it has its basis in physics; each decision we make was a neuron firing due to patterns of electro-chemical stimuli resulting in a chemical signal being sent out to cause us to respond in a hard-wired nature. The issue is not that physics equations and concepts can't explain it; they can. It's moreover the fact that it happens on such a large and complex scale that we as a species favor models and patterns that we deem simpler and useful as opposed to the trillions of cause-and-effect reactions that produce a decision.

Essentially, what I am saying is that I personally enjoy physics because it is at its very root the examination of reality. While I'm not saying sociology and the humanities isn't interesting or valid, physics interests me because it not only tells me what will happen, but also what is actually causing this to happen. Physics isn't just a model for what happens, it is what happens. I'm not saying I'm about to crunch numbers into an equation and tell you why a thief robbed a store, but I am saying that the physics is there, it's just staggeringly complex. To me, physics is as pure as knowledge gets. There is nothing that exists which cannot trace itself back to physics (and as an extension, mathematics and pure logic) because in the end, physics is the science of existence.

And if it's a philosophical discussion you want, it's one you've got because what I've just argued is in essence Physicalism/Materialism.

[Agares Tretiak]

Yes physics shows really, that the more you try to predict certain things, the less likely you are to predict the results. Quantum uncertainty principle, I think it's called, though I won't claim to be conversant in the technical terms of physics.

Sociology, for instance, examines a vast array of possible factors from various points of view to examine social interactions. THere is, of course, a scientific approach to ascertaining these factors, proof of or to the contrary of various theories, and a very long and growing awareness of societal mechanics. In fact, one can argue that large groups of people are far easier to accurately predict and determine their course of actions, than smaller groups or individuals. It would be, I think, impossible to take a single sociological statistic and use it to prove, however, that mere physical attributes alone attribute or are the sole cause of various tendencies in a person.

People have the remarkable ability to make choices, which places them at odds with the idea that people can be defined by pure physical criteria. Admittedly, people with the sort of willpower to work against what might be dictated as their nature may be difficult to define, they certainly exist. Furthermore, large groups can, at times, move in completely unpredictable directions. Is this a failing of human knowledge concerning the physical criteria necessary to generate such mass responses, or does it mean that there's some determinism in human nature?

Such a question is difficult to answer at this time.

History demonstrates, time and again, that with closer examination, people do not fit into neat little categories, but are comprised of hundreds, if not thousands of variables that can defy the conventions of logic. Furthermore, history shows, even in this modern age, fact alone cannot determine or direct humanity on the best course. Rationality could be argued to have clear set boundaries when working with humans, since rationality is not the only or primary criteria for most people to make choices.

In my studies I've learned that no single system is capable of providing a complete answer in regards to the two realities people inhabit. The purely physical world that can be described through measurements and rational examination, and the world we have always inhabited based on perception and emotion. To try to separate the two is to deny an entire half of truth. These leads me to believe the only way to really see the truth is to know the limitations of both perspectives and merge them in a holistic approach to the universe.

OR maybe I just pulled this whole argument out of my ass.

[Cygna]

[Scientific Waffle]

D: but Intus, we're given them what they want and going into a philosophical discussion, with the bonus being that it centers around physics in relation to truth and reality! ;_;

Agares, I'm not arguing determinism. The name of the phenomenon you're referring to it Heisenberg's uncertainty principle, which does indeed state that at the most basic of levels, physics cannot perfectly predict the future. My viewpoint is that the "intangibles" you refer to, human choice, emotion, etc, are macroscopic manifestations of incredibly complex systems of events described in physics. However, that does not mean that every choice you make is predetermined; physics itself dictates probability and uncertainty. However, when events happen and choice are made, these actions are all the results of physics that happens. We tend to reject that something such as the decision to eat cake or vote for a candidate is something transcendent of physical phenomena; in my view it's just so staggeringly complex that what is in reality seemingly infinite logical events seems to manifest itself in a seemingly (but not truly) illogical reaction.

In the end, human choice is not always rational, but what causes humans to choose so is.

[Cygna]

D: but Intus, we're given them what they want and going into a philosophical discussion, with the bonus being that it centers around physics in relation to truth and reality! ;_;

Okay. Besides, all of the posts so far have been very interesting. Do continue.