Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Coulomb Potential Energy - discrepancy between like and opposite charges

  1. Jun 3, 2010 #1
    The Coulomb potential energy between two point charges is defined as:


    Suppose that you have two equal, like charges at a distance L, then V_like=q2/(k*L)

    Similarly, for two equal, opposite charges, V_opp=-q2/(k*L)=-V_like

    Both situations experience a force of equal magnitude (just opposite directions), yet V_opp<V_like? Shouldn't the two potential energies be equal?

    By analogy with a mechanical spring, a weight that is left of the equilibrium position experiences a force of equal magnitude but opposite direction to a weight on the right of the equilibrium position. This is similar to the potential energy above. However, in this case, V_left=V_right, since the spring potential energy is:

    V = 0.5kx2
  2. jcsd
  3. Jun 3, 2010 #2


    User Avatar
    Homework Helper

    Force is actually related to the derivative of the potential energy. The actual value of the potential energy doesn't matter at all. If you take the derivative of V with respect to position, you'll see that for like charges, it is the opposite of the derivative for unlike charges. Same with the mechanical spring: the derivative of V is the opposite for the mass on the left as for the mass on the right.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook