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Charge released from rest near a grounded conductor

  1. Oct 19, 2008 #1
    1. The problem statement, all variables and given/known data
    A charge q of mass m is released a distance d from a semi-infinite grounded conductor. How long will it take the charge to reach the conductor?

    So I tried this using the method of images, and I can easily find the force on the charge a distance d away:

    F = -q^2 zhat / (4 pi epsilon0 (2d)^2)

    But I'm not sure where to go from here.

    Any help would be fantastic
     
    Last edited: Oct 19, 2008
  2. jcsd
  3. Oct 20, 2008 #2
    [tex]F= - \frac{q^2}{4 \pi \epsilon_0 (2d)^2}\hat{z}[/tex]
    [tex]F = m \frac{\partial^2 r}{\partial t^2}[/tex]

    Does this help??

    Sam =]
     
  4. Oct 20, 2008 #3
    Not really, I'm aware of the definition of Force. If you'd like to show how to integrate that I'd be grateful, but I have no idea.
     
  5. Oct 20, 2008 #4
    d is a constant here: instead, write the force as a function of the variable z (the variable distance to the conductor). Then, as an intermediate step, can you get an equation for the velocity dz/dt of the charge as a function of z?
     
  6. Oct 20, 2008 #5
    Thanks that was what I needed to do.

    Just as a followup:
    change second derivative of z to dv/dz*dz/dt=dv/dz*v
    from there it's pretty easy
     
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