Question

You are given a total charge Q. How do you divide it into two parts so that the force between them is maximum

Answer 1

Answer:

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Answer 2

first part Q/2 and the other is Q/2

let first part is x and the other is (Q - x) are seperated r distance.

so force between them, F = kx(Q -x)/r² = k(Qx - x²)/r²

differentiating with respect to x,

dF/dx = k(Q - 2x)/r²

when dF/dx = 0, x = Q/2

at x = Q/2, d²F/dx² < 0

hence, at x = Q/2 force will be maximum.

so, first part is x = Q/2 and the other is (Q - x) = Q - Q/2 = Q/2

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