# A charged wire exerts force on a proton.

1. Nov 7, 2011

### joe41442

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)?