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Central potential 
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#1
May210, 12:48 PM

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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.. 


#2
May210, 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 ∞). 


#3
May310, 04:58 AM

P: 3

Thank you for the reply tinytim.
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 


#4
May310, 05:06 AM

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P: 26,151

Central potential
I'm sorry, I don't understand.



#5
May310, 05:20 AM

P: 3

Me, too



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