A charge Q is divided into two parts, q and (Q - q). The repulsion between them is maximum when Q : q is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2 : 1
By Coulomb's law, the force between the two parts kept a distance \( r \) apart is proportional to the product of the charges.
\( \displaystyle F = \frac{k\,q\,(Q - q)}{r^{2}} = \frac{k}{r^{2}}\left(Qq - q^{2}\right) \)
For a maximum, the derivative with respect to \( q \) is zero:
\( \displaystyle \frac{dF}{dq} = \frac{k}{r^{2}}\left(Q - 2q\right) = 0 \;\Rightarrow\; q = \frac{Q}{2} \)
The second derivative \( -2k/r^{2} \) is negative, so this is a maximum. The charge is split into two equal halves, and
\( \displaystyle Q : q = Q : \frac{Q}{2} = 2 : 1 \)
Note: The same question was also asked in CUET (UG) 2026 on 19-05-2026 (Slot 1).