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Properties of Charges

A charge Q is...

Question

A charge Q is to be divided between two objects. What should be the values of the charges on the objects so that the force between the objects can be maximum?

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Solution

Suppose one object receives a charge q and the other Q-q. The force between the objects is given by
$F = \frac{k (Q - q) q}{d^{2}}$
For F to be maximum, $\frac{d F}{d q} = 0 \Rightarrow Q - 2 q = 0 ∴ q = \frac{Q}{2}$

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