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

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$\frac{{(N - 1)}^{2}}{4 N^{2}}$

$\frac{4 N^{2}}{(N - 1)}$

$\frac{N^{2}}{4 (N - 1)}$

$\frac{2 N^{2}}{(N - 1)}$

answer is C.

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Detailed Solution

For $F_{max}, q_{1} = q_{2} = \frac{Nq}{2}$ and
For $F_{min}, q_{1} = (N - 1) q, q_{2} = q$
$\frac{F_{max}}{F_{min}} = \frac{{(\frac{N}{2} q)}^{2}}{(N - 1) q \times q} = \frac{N^{2}}{4 (N - 1)}$

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