physics

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

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one is x
other is q-x

F = kx(q-x)/d^2 where k and d are constants

dF/dx = (k/d^2) [ x(-1) +(q-x)1]
max when dF/dx = 0
0 = -x + q - x
q = 2 x
x = q/2
evenly divided

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