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I've never been good at "Find the maximum whatever" (Area, charge in this case, etc...) type problems, so I could use some coaching on this one.

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?

q = Q/2, Fmax = kQ^2/4r^2

Admittedly it's been pretty rough going on this one, and it's only the 3rd homework problem of the semester... but I've resolved to get through it all somehow. Through using the text's website companion I've gotten it down to the final step, which is where I get stumped. I've got it all down to:

k/r^2(qQ - q^2) = (3/4) (kQ^2/4r^2)

At this point the interactive help says all I gotta do is solve for q. But I can't seem to get q by itself. How can I manipulate the equation in order to isolate q? I tried a few things, such as dividing both sides by k to eliminate k, then multiplying both sides by r^2 to eliminate r^2. However, at that point I get stumped and have no idea how to further simplify the equation. Any help would be appreciated.

## Homework Statement

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?

## Homework Equations

q = Q/2, Fmax = kQ^2/4r^2

## The Attempt at a Solution

Admittedly it's been pretty rough going on this one, and it's only the 3rd homework problem of the semester... but I've resolved to get through it all somehow. Through using the text's website companion I've gotten it down to the final step, which is where I get stumped. I've got it all down to:

k/r^2(qQ - q^2) = (3/4) (kQ^2/4r^2)

At this point the interactive help says all I gotta do is solve for q. But I can't seem to get q by itself. How can I manipulate the equation in order to isolate q? I tried a few things, such as dividing both sides by k to eliminate k, then multiplying both sides by r^2 to eliminate r^2. However, at that point I get stumped and have no idea how to further simplify the equation. Any help would be appreciated.

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