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 oscillating on a spring

  1. May 9, 2012 #1
    1. The problem statement, all variables and given/known data

    (a) Consider an oscillating electric dipole of moment p(t)=p0sinωt. At large distances r>>c/ω from the dipole, the magnetic potential in the Lorenz gauge is

    A(r,t) = [itex]\frac{\omega \cos\omega(t-r/c))\bf{p_0}}{4\pi r c} [/itex]

    Calculate the E and B fields, and deduce the Poynting vector, showing that it points radially outwards and vanishes on the axis of the dipole.

    (b) A small body of mass m and charge q hangs from the ceiling by a spring with spring constant k. The body is initially at rest, a distance h from a very cold floor, h>>mc^2/k. At time t= 0 it is given a slight downwards kick so that executes tiny oscillations with amplitude d<<h. Calculate the average intensity of the electromagnetic radiation hitting the floor as a function of the radial distance R from the point on the floor directly below the particle.



    2. Relevant equations

    Clearly the motion of the particle is given by z = dsinωt with ω=sqrt(k/m).



    3. The attempt at a solution

    I've done all of part (a), which was fairly trivial. However for part (b) I am somewhat confused. Can you just treat the particle as an oscillating dipole, (with moment dqsinωt) with the relevant E and B fields be that as calculated in part (a)? If so, then to calculate the intensity on the floor, do you set r = h, and then average out the power, and divide by pi*R^2?

    I hope these questions make sense.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Charge oscillating on a spring
  1. Oscillating Springs ? (Replies: 1)

Loading...