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Im having trouble setting up the problem..any help would be appreciated.

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- Thread starter suspenc3
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- #1

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Im having trouble setting up the problem..any help would be appreciated.

- #2

Hootenanny

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What are you intial thoughts?

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- #4

Hootenanny

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[tex]I = \frac{S}{r^2} + \frac{3S}{(10-r)^2}[/tex]

Perhaps something like that?

Perhaps something like that?

- #5

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Yes, that makes sence, but what can I use to eliminate one of the variables?

- #6

Hootenanny

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[tex]I\;\; \alpha \;\; \frac{S}{r^2} + \frac{3S}{(10-r)^2}[/tex]

As, S is constant, the only two variables are I and r. We want to know how I varies with respect to r, if I understant the problem correctly?

So how about finding [itex]I'(r)\;\;dr[/itex]?

- #7

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[tex] I' = \frac{-10r^2}{r^4} - \frac{30(r^2-2r+100)}{(r^2-2^r+100)^2}[/tex]

When I try to solve for r I dont get a real number

- #8

Hootenanny

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I get

[tex]I'(r) = \frac{6S}{(10-r)^3} - \frac{2S}{r^3}[/tex]

You don't want to solve for I. What do you know about the gradient at a minimum point?

[tex]I'(r) = \frac{6S}{(10-r)^3} - \frac{2S}{r^3}[/tex]

You don't want to solve for I. What do you know about the gradient at a minimum point?

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- #9

Hootenanny

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If you are having trouble visulaising the functions I have attached plot of them. The blue curve is that of the original function, the red is that of the derrivative. As S is constant(strength of source) I assigned an arbitray value of S=1 for this plot.

Hope this helps

Hope this helps

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