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A charged wire exerts force on a proton.

  1. Nov 7, 2011 #1
    1. The problem statement, all variables and given/known data
    An electrically charged wire on the z axis exerts a force on a proton, which moves on the x axis. The initial conditions for the proton position and velocity are:
    x(0) = x0 and v(0) = 0.

    The force on the proton is Fx(x) = C /x where C = 3.2×10−15 Nm.

    (A) Determine the potential energy function, U(x). Choose x0 to be the reference point; i.e., U(x0) = 0.
    (B) Calculate the velocity v at the time when the proton passes the point x = 2 x0.
    (C) Calculate the time t when the proton passes the point x = 2 x0. Assume x0 = 1 m.


    2. Relevant equations
    E= (1/2)m*v^2 + U(x)
    U(x)= -∫F(x)dx
    dx/dt= ±√[(2/m)(E-U(x))]


    3. The attempt at a solution
    In part A I integrated F(x) and got U(x)= -C*ln(x)
    In part B I used dx/dt= ±√[(2/m)(-C*ln(x))]
    In part C I'm trying to integrate dx/dt= ±√[(2/m)(-C*ln(x))] but I really have no idea on what to do. I looked up the integral of 1/√(lnx) on wolframalpha and it said that it integrates out to some imaginary error function? Is there some other way I could find t or x(t)?
     
  2. jcsd
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