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Central potential

by mystraid
Tags: central, potential
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mystraid
#1
May2-10, 12:48 PM
P: 3
Hello,

I am trying to compute the potential for a central force of the form: F(r) = f(r)r
where r=|r|

Using the conservative force information, equation1 comes for potential V(r):

equation1: V(r) = [tex]\int [/tex] (-F(r))= [tex]\int [/tex] (-f(r) r)

In wikipedia it is stated that this integral is bounded from |r| to infinity. However I could not understand the reason.

Could someone help me?
Thanks..
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tiny-tim
#2
May2-10, 02:57 PM
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Hello mystraid! Welcome to PF!

It has to be bounded from |r| to somewhere

we can choose that somewhere to be anywhere, but it makes it simplest if we choose it to be ∞ (so the potential is always 0 at ∞).
mystraid
#3
May3-10, 04:58 AM
P: 3
Thank you for the reply tiny-tim.

And, I have another question. What if the function is dependent on the position vector r but not the magnitude of it?

So:

F(r) = f(r)r

Then is there any potential for such a force, and if so, under what conditions it exists?

Thanks

tiny-tim
#4
May3-10, 05:06 AM
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Central potential

I'm sorry, I don't understand.
mystraid
#5
May3-10, 05:20 AM
P: 3
Me, too


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