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from the equation V^2 = 2(-e) [ (1/4 pi Eo) ( -e / r + -e / r )] / m why is V sq

ID: 1725618 • Letter: F

Question

from the equation V^2 = 2(-e) [ (1/4 pi Eo) ( -e / r + -e / r )]       /    m why is V squared by 2?? i dont understand... what is the physics of the problem, that u have to make Vsquared? and i dont understand why theres a 2 behind (-e),, why do wetimes that equation by 2??? from the equation V^2 = 2(-e) [ (1/4 pi Eo) ( -e / r + -e / r )]       /    m why is V squared by 2?? i dont understand... what is the physics of the problem, that u have to make Vsquared? and i dont understand why theres a 2 behind (-e),, why do wetimes that equation by 2???

Explanation / Answer


   for simplicity we use the conservation of energytaking the potential energy to be zero when the moving electron isfar
   away from the fixed electrons
   the final potential energy will be
   Uf = 2 e2 / 4 o d
   where d is half the distance between the fixedelectrons
   the initial kinetic energy is
   Ki = (1 / 2) m v2
   where m is the mass of the electron and v is theinitial speed of the electron
   the final kinetic energy is zero
   thus
   Ki = Uf
        = (1 / 2) mv2   
    = 2 e2 / 4 o d
   solve for v