1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

E&M Griffiths 3.34

  1. Nov 9, 2005 #1
    A point charge (q, mass m) is released from rest at a distance d from a grouned infinite conducting plane. How long does it take to hit the plane?
    Answer pi*(d/q)*sqrt(2pi*eps m d)
    This problem seemed easy to me at very, but it leads to a second order nonlinear equation
    [tex]m\frac{d^2 z}{dt^2} = \frac{q^2}{16 \pi \epsilon_0 z^2}[/tex].

    I tried using energy considerations to write v as v(z), I then solved for z as z(v), and integrated the above equation for v(t), putting in the limits 0 and infinity. This did not give the correct answer, although it appeared to be close. Any suggestions?
  2. jcsd
  3. Nov 10, 2005 #2
    I haven't actually worked out the problem, so I'm not sure if the right side of your equation is correct. Just as a note incase you didn't do this - since the infinite conducting plane is grounded, you need to use the method of images to get your potential function.
  4. Nov 10, 2005 #3
    Maple choked on the d.e. but, you should be able to show
    v2 = 2c(1/z - 1/d) with c = q2/(16 Pi Eps0 m)
    with conservation of energy or integrating the force equation once.
    now to solve for time put solve for v and use the positive root,
    the negative one leads to t<0.
    thus [tex] t = \frac{1}{\sqrt{2c}} \int_d^0 \sqrt{ \frac{ dz}{ d - z}} \. d z [/tex]
    The substitution z = d cos2(theta) makes this doable.
  5. Nov 10, 2005 #4
    Yeah, that's what I indicated I tried above. It appeared to fail the first time I did it, but the second time it worked out.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: E&M Griffiths 3.34
  1. Griffiths 2.26 E&M (Replies: 0)

  2. Griffiths Problem 3.34 (Replies: 6)