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So I was studying for this electromagnetism test I have tomorrow, and I came across this problem about a charged soap bubble, and I looked the solutions manual and it looks all handy wavy and boring, so I tried to force my way into it and I ended up with this other problem, which seems a lot more interesting.
Basically the problem is: Find a function [math] D(\theta,R) [/math] which express the distance in red(where R is the radius of the circle).
>pic related
So I was able to determine some boundary conditions for it and also to force them on a guessing function gnuplot, however its just a fit, and they are probably wrong. So I leave it to you geometry /sci/entists, please enlighten me with some elegant analytical solution.
Here is a set of boundary conditions to fasten you up:
[eqn]D(0)=2R[/eqn]
[eqn]D\left( \frac{\pi}{4}\right)=2R[/eqn]
[eqn]D\left( \frac{\pi}{2}\right)=0[/eqn]
[eqn]\frac{d }{d\theta}D(0,R)=0[/eqn]
Thank you, gg.
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The derivative in the first term is actually a partial derivative, also I'd like to say that there is one more boundary condition, but I am NOT SURE the function has to obbey it, but if does then the electro problem could be solved in a very elegant manner so, bonus points if it obbeys:
[eqn]\frac{2}{\pi} \int_{0}^{\frac{\pi}{2}}D(\theta,R)d\theta=R\sqrt{2}[/eqn]
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>>8743211
D(pi/4) isn't 2R.
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>>8743211
You have from the cosine law
[math]R^2 = R^2 + D^2 -2RDcos(\theta)\\
\\
\therefore
D(c,R)=2Rcos(\theta)
[/math]
Either you are overthinking it or I'm an idiot.
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>>8743286
He's overthinking it. It's easy to see even without the cosine law. I guess everyone has these blind moments sometimes.
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You brought dihonol delet thread and kys
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