# Charge Maximization

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• Jan 15th 2009, 12:34 PM
Aryth
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 $\displaystyle \frac qQ$ will the electrostatic force between the two spheres be maximized?
• Jan 15th 2009, 02:55 PM
TheMasterMind
Quote:

Originally Posted by Aryth
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 $\displaystyle \frac qQ$ will the electrostatic force between the two spheres be maximized?

Consider this

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

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

$\displaystyle Q-2q=0$

$\displaystyle q=\frac{Q}{2}$

$\displaystyle =\frac{1}{2}$

Does that work? It's been a while since I've solved this kind of problem excuse me if it has a fault
• Jan 15th 2009, 04:07 PM
Aryth
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.
• Jan 15th 2009, 07:02 PM
TheMasterMind
Quote:

Originally Posted by Aryth
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.
• Jan 19th 2010, 01:16 PM
NBrunk
Quote:

Originally Posted by TheMasterMind
Consider this

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

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

$\displaystyle Q-2q=0$

$\displaystyle q=\frac{Q}{2}$

$\displaystyle =\frac{1}{2}$

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.
• Jan 25th 2010, 12:16 PM
Aryth
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.