I've been reading Rutherford's and Thomson's work on atomic models for a research paper I'm doing, and I am confused on how they derived the equation for the average angle of deflection, φ = (π/ 4) (NeE/ mu^2) ·( 1 /R). and φ = (π/ 4) (e^2/ mv^2) ·( Ne/b). Rutherford cites Thomson and as far as I've read Thomson waves it as 'easy to prove.' I would like to know from what laws/ equations are they deriving this from and how. If possible, a step-by-step derivation would be greatly appreciated.

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