Acharge q is to be divided into two parts, labeled 'q' and 'q-q? what is the relationship of q to q if, at any given distance, the coulomb force between the two is to be maximized?

Explanation:

The two charges are q and Q - q. Let the distance between them is r

Use the formula for coulomb's law for the force between the two charges

So, the force between the charges q and Q - q is given by

For maxima and minima, differentiate the force with respect to q.

For maxima and minima, the value of dF/dq = 0

So, we get

q = Q /2

Now

the double derivate is negative, so the force is maxima when q = Q / 2 .

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