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!

Potential energy of a dipole point and point charge

  1. Oct 18, 2012 #1
    1. The problem statement, all variables and given/known data
    A point dipole p is at the origin of coordinates, while a point charge q is at position r. Calculate the potential energy U of this system in two ways (a) by treating the dipole as a source and q as a test charge in the dipole field (b) by treating the dipole as a test-object in the Coulomb electric field of the point-charge, now treated as a source


    2. Relevant equations
    U=-pE
    V(r)=Integral of Edr

    3. The attempt at a solution
    I found the potential

    V(r)=p.r/(4πε0r^3)=p.r(hat)/(4πε0r^2)=pcosθ/(4πε0r^2)

    Then I differentiated since E(r)=d/dr(V(r))

    E(r)=-d/dr(V(r))=-d/dr(pcosθ/(4πε0r^2))=-(-3pcosθ/(4πε0r^3))=3pcosθ/(4πε0r^3)

    So my U would be equal

    U=-pE=-p(3pcosθ/(4πε0r^3))=-3p^2cosθ/(4πε0r^3) ????

    It doesn't make sense
     
  2. jcsd
  3. Oct 18, 2012 #2
    First, [itex]\vec{E}= -\nabla \Phi \ne -\frac{\partial \Phi}{\partial r}[/itex].
    Second, the energy of a charge q in potential V is [itex]U=qV[/itex].
    Third, the energy of a dipole p in field E is [itex]U=-\vec{p}\cdot\vec{E}[/itex].
    For part a, you're supposed to use a charge q in a dipole field.
    For part b, you're supposed to use a dipole [itex]\vec{p}[/itex] in point charge field.
     
  4. Oct 25, 2012 #3
    Thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Potential energy of a dipole point and point charge
  1. Point charge potential (Replies: 1)

Loading...