a
(a) Suppose neutral point \(N\) lies at a distance \(x\) from dipole of moment \(p\) or at a distance \(x_2\) from dipole of \(64\) \(p\).
At \(N\) \(|E. F.\) due to dipole \(1|= |E. F.\) due to dipole \(2|\)
\(==>\) \(\frac{1}{{4\pi {\varepsilon _0}}}.\frac{{2p}}{{{x^3}}} = \frac{1}{{4\pi {\varepsilon _0}}}.\frac{{2(64p)}}{{{{(25 - x)}^3}}}\)
\(==>\) \(\frac{1}{{{x^3}}} = \frac{{64}}{{{{(25 - x)}^3}}}\) \(==> x = 5\, cm\)