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!

Homework Help: Deriving an expression for the energy required to separate charges

  1. Feb 27, 2017 #1
    1. The problem statement, all variables and given/known data
    Hi guys, would just too make sure my derivation and insight to why is correct.
    Question: a) only


    2. Relevant equations

    3. The attempt at a solution
    $$dU=-F_{ext} \cdot dx$$
    Now as the ##F_{ext}## is in the same direction and the direction vector { have not figured how to put direction vector in} then the equation becomes ##dU=-Fdx## this assume the direction is along the x axis
    So now if I intergrate both sides ##\int_{U(a)}^{U\infty}dU=-\int_{a}^{\infty}Fdx##

    Subbing in a factoring columbs force law I get:


    Now U infity is zero because there is no force acting on it anymore and so I am left with##-U(a)## on the LHS on the RHS I am left with ##-kq_1q_2\frac{1}{a}##
    thus the two negative cancel and I am left with the electric poteinal energy. Is this correct?
  2. jcsd
  3. Feb 27, 2017 #2


    User Avatar
    2017 Award

    Staff: Mentor

    If your answer has a positive sign, it is correct.

    Beyond the scope of your homework problem: (c) has a very interesting story. The naive way to improve the estimate leads to something that is not well-defined in mathematics, and you have to be careful how to do it properly to get the correct result.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted