N fundamental charge each of charge 'q' are to be distributed as two point charges seperated by a fixed distance then the maximum to minimum force bears a ratio ( N is even and greater than 2 )

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Solution

Let charges be $Q_{1} = n q$ and $Q_{2} = (N - n) q$

$F = \frac{k Q_{1} Q_{2}}{r^{2}}$

$F = \frac{k n (N - n) q^{2}}{r^{2}} = \frac{k q^{2}}{r^{2}} n (N - n)$

For maximum force, the differential of $F$ w.r.t $n$ should be $0$ .

$⟹ N - 2 n = 0$

$⟹ n = \frac{N}{2}$

Hence, $Q_{1} = Q_{2} = \frac{N q}{2}$

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N fundamental charge each of charge 'q' are to be distributed as two point charges seperated by a fixed distance then the maximum to minimum force bears a ratio ( N is even and greater than 2 )

Let charges be Q1=nq and Q2=(N−n)qF=kQ1Q2r2F=kn(N−n)q2r2=kq2r2n(N−n)For maximum force, the differential of F w.r.t n should be 0.⟹N−2n=0⟹n=N2Hence, Q1=Q2=Nq2