November 24th, 2016, 01:15 AM  #1 
Newbie Joined: Nov 2016 From: belgrade Posts: 2 Thanks: 0  POTENTIAL: sum ∑ to integral
Hi, I'm new to this forum. I have a task to do: positive charged particle (proton in this case) is traversing throught channel in crystal lattice ((100) direction in FCC crystal for example). But in my case thing is little more simple: positive particle i passing near row (string) of atoms that are all on same spacing "d". 123.jpg Total potential is sum of all potentials from every single atom in row: U(total) = ∑ Ui(Ri), where Ri is distance from positive particle to ith atom in row. So sum goes from first particle in row to last particle in row, and "i" is number of particles in row. How come that this sum can be changed with integral? Integral is: 111.jpg What is procedure, step by step for this equation? Thank You, Nikola 
November 24th, 2016, 09:40 AM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,597 Thanks: 620 Math Focus: Wibbly wobbly timeywimey stuff. 
Please do not double post. Dan 

Tags 
∑, integral, potential, sum 
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