Question

two electric dipoles of moment P and 64 P are placed in opposite directions on a line at a distance of 25 cm. The electric field will be zero at point between the dipoles whose distance from dipole of moment P is

Answer 1

$$\begin{gathered} \mathrm{Electric}\mathrm{field}\mathrm{is}\mathrm{proportional}\mathrm{to}\frac{\mathrm{p}}{{\mathrm{d}}^3}. \\ \mathrm{Hence},\mathrm{the}\mathrm{required}\mathrm{condition}\mathrm{for}\mathrm{zero}\mathrm{electric}\mathrm{field}\mathrm{is}, \\ \frac{\mathrm{p}}{{\mathrm{x}}^3}=\frac{64\mathrm{p}}{{\left[25-\mathrm{x}\right]}^3} \\ {\left[\frac{25-\mathrm{x}}{\mathrm{x}}\right]}^3=\frac{64\mathrm{p}}{\mathrm{p}} \\ \left[\frac{25-\mathrm{x}}{\mathrm{x}}\right]={\left(64\right)}^{1/3} \\ \left[\frac{25-\mathrm{x}}{\mathrm{x}}\right]=4 \\ 25-\mathrm{x}=4\mathrm{x} \\ 5\mathrm{x}=25 \\ \mathrm{So},\mathrm{x}=5\mathrm{cm} \end{gathered}$$