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!

Lienard-Wiechert potential for 2 discrete Qs

  1. Oct 25, 2007 #1
    I've tried a simple derivation of the Lienard-Wiecher potential for 2 discrete charges seperated by dr, but end up with a result which isn't the same as the theoretically correct version:

    Take two charges q1 @r1, q2 @r2 with r1 > r2, dr = r1 - r2, parallel
    and both travelling at velocity v away from and along r1, r2. The
    observation point is at r = 0. The potential of q1 that arrives at q2
    is from a retarded time t' = dr/(v + c). This is when q1 was at r2 +
    dr - vt' = r2 + dr - v dr/(v + c) = r2 + dr/(1 + B) where B = v/c. So
    the potential at the observation point can be replaced by an
    equivalent static q1 and q2 seperated by dr/(1 + B), equivalent to
    increasing the charge density by (1 + B) at r.

    The total potential is then q2/r2 + q1/(r2 + dr/(1 + B)) which for
    small dr and q1 = q2 = q can be written using the first two terms of a taylor expansion:


    q/r2 + q/r2 (1 - dr/(1 + B)r2)


    = 2q/r2 - q dr/(1 + B)r2^2 )


    I'm not sure how to proceed further, since I was hoping to end up with
    an expression 2q/(1 + B) r2. Can anyone see where I've gone wrong?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Lienard-Wiechert potential for 2 discrete Qs
  1. Orbits and potential (Replies: 0)

  2. Potential Energy (Replies: 0)

  3. More Vector Potential (Replies: 0)

Loading...