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Binomial expansion of relativistic formula

  1. May 4, 2010 #1
    1. The problem statement, all variables and given/known data
    The speed v of electrons from a high energy accelerator is very near the speed of light c. Given the voltage V of the accelerator, calculate the ratio v/c. The relativistic formulafor this calculation is (see relevant equations)

    Use the binomial series to find (1-v/c) in terms of V


    2. Relevant equations

    v/c = (1-(1/4V^2))^0.5


    3. The attempt at a solution

    v/c = (1-(4v^2)^-1)^0.5 = (approx) [1- (1/8V^2) + (3/128V^4) - (15/3072V^6)]

    therefore;

    1-v/c= (1/8V^2) - (3/128V^4) + (15/3072V^6) = 1.25x10^(-17)
     
  2. jcsd
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