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Math Help - Charge Maximization

  1. #1
    Super Member Aryth's Avatar
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    Charge Maximization

    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 \frac qQ will the electrostatic force between the two spheres be maximized?
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  2. #2
    Member TheMasterMind's Avatar
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    Quote Originally Posted by Aryth View Post
    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 \frac qQ will the electrostatic force between the two spheres be maximized?
    Consider this



    \frac{dF(q)}{dq}=0

    0=\frac{dF}{dq}=\frac{K}{r^2} \frac{d}{dq} (qQ-q^2)

    <br />
Q-2q=0

    q=\frac{Q}{2}

    <br />
=\frac{1}{2}

    Does that work? It's been a while since I've solved this kind of problem excuse me if it has a fault
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  3. #3
    Super Member Aryth's Avatar
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    Your answer is correct. We have to use that to get to the equation for the maximum force. And we were given that answer, we just had to derive it. And your method works perfectly. Thanks for the help.
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  4. #4
    Member TheMasterMind's Avatar
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    Quote Originally Posted by Aryth View Post
    Your answer is correct. We have to use that to get to the equation for the maximum force. And we were given that answer, we just had to derive it. And your method works perfectly. Thanks for the help.
    No Problem. I am happy my memory is not deceiving me.
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  5. #5
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    Quote Originally Posted by TheMasterMind View Post
    Consider this



    \frac{dF(q)}{dq}=0

    0=\frac{dF}{dq}=\frac{K}{r^2} \frac{d}{dq} (qQ-q^2)

    <br />
Q-2q=0

    q=\frac{Q}{2}

    <br />
=\frac{1}{2}
    I have the same problem and don't quite understand how you figured out that (qQ - q^2) is what you're supposed to be taking the derivative of. Could anyone explain it a little please? It'd be very appreciated.
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  6. #6
    Super Member Aryth's Avatar
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    The reason why is because you are taking the derivative with respect to q, and (qQ - q^2) are the only terms in the equation with q in them, so they cannot "exit" the derivative without being differentiated.
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