When \(C\) is placed in contact with \(A\), charge on \(A\) and \( C\) will be \(=\frac{ q }{2}\)

Now \(C\) is placed in contact with \(B\), charge on \(B\) and \(C\) will be \(=\frac{q+\frac{q}{2}}{2}=\frac{3 q}{4}\)

\(F ^{\prime}= F _{2}- F _{1}=\frac{\left( K \frac{3 q }{4}- K \frac{ q }{2}\right)}{\frac{ r ^{2}}{4}} \cdot \frac{3 q }{4}\)

\(=\frac{3 Kq ^{2}}{4 r ^{2}}=\frac{3 F }{4}\)