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Coulomb's Law and spheres Problem

  1. May 29, 2007 #1
    1. The problem statement, all variables and given/known data

    Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated as particles. For what value of q/Q will the electrostatic force between the two spheres be maximized?

    2. Relevant equations

    (k)(q1q2)/r^2

    3. The attempt at a solution

    I posted a similar problem concerning an electric field some time ago, and am attempting to use the same solution, that is, taking the derivative of the equation I end up with, but the derivative ends up being zero for me. I end up with:

    k(Q-q)q / r^2

    And then after factoring out k/r^2, I'm left with just (Q-q)q. I tried doing a derivation using the product rule, but I just end up with zero. When I try to derive this, I get:

    1 * (1-1) + (Q-q) which just leaves me with Q - q, which is not the answer. What am I doing wrong?
     
  2. jcsd
  3. May 29, 2007 #2
    You differentiated the equation with respect to...?
     
  4. May 29, 2007 #3
    Ah nevermind, upon multiplying the q back into the (Q-q) and then deriving, I get the correct answer. However, can it be said as a rule of thumb that you should factor AFTER taking the derivative, or are there situations where you should factor beforehand?
     
  5. May 29, 2007 #4
    Basically I used df/dq.
     
  6. May 29, 2007 #5
    There's no difference between: [tex]\frac{d}{dq}\left(q(Q-q)\right)[/tex] and [tex]\frac{d}{dq}\left(qQ-q^2\right)[/tex], and this holds true no matter what kind of functions are in the product. (They should be continuous of course.)
     
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