1. Limited time only! Sign up for a free 30min personal 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!

Charge moving toward a conductor. Solution makes no physical sense!

  1. Oct 10, 2013 #1
    This is not an assigned homework problem, just something I came across. It's in Griffiths E&M book.
    Also I apologize if my equations don't look right. They are showing up all weird on my computer screen.

    1. The problem statement, all variables and given/known data

    A point charge q of rest mass mass m is released from rest a distance d from an infinite grounded conducting plane. How long will it take for the charge to hit the plane?

    2. Relevant equations

    F=k (q_1 q_2)/r^2 =m[r]\ddot{}[/itex]


    3. The attempt at a solution
    The solution is given as

    (πd/q) √(2πϵ_0 md)

    Griffth implies that we should use the method of images, comparing the problem to two oppositely charged particles moving toward each other. I can get the solution by solving the differential equation above. In fact, mathematically the only solution to that is that r as a function of time comes out to r being some constants times t to the 2/3 power. The problem is that it doesn't seem to be a real physical solution! It implies that r gets bigger as time goes forward, which is not the case. also, if you then differentiate that equation to find v as a function of t, we'll get v as some constants times t to the -1/3 power. This implies that v decays as time goes forward, which can't be true. The charge has to be gaining speed as it falls right? Same with acceleration. Shouldn't it be gaining acceleration as it gets closer to the sheet?

    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 10, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    A minus sign is missing from the equation: The mirror charge is opposite to the real one, so the force points inward, towards the plane.


    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Charge moving toward a conductor. Solution makes no physical sense!
  1. Moving charge. (Replies: 4)

Loading...