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Q)Given that q1+q2=q. For what ratio q1/q will the force between q1 and q2 be maximum?

Hello Ishaan,

We have to assume that the distance between the 2 charges remains constant. So the force varies as the product of q1 and q2. So, for what value of q1 does the following function have a maximum:

f(q1) = q1*q2

Since q2 = q - q1, the function can be rewritten

f(q1) = q1*(q - q1) = q*q1 - q1^2

Setting the first derivative equal to zero will tell us when the slope of the function is zero and therefore either a maximum or minimum. Since q is a constant, the first derivative is

f'(q1) = q - 2q1

Setting that equal to zero we find that q1 = q/2.

We can find if that is a minimum or maximum from looking at the 2nd derivative.

f''(q1) = -2

Since the 2nd derivative is negative, f(q1) is maximum when q1 = q/2.

I hope this helps,

Steve

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