A point $$Q$$ lies on the perpendicular bisector of an electric dipole of dipole moment $$p.$$ If the distance of $$Q$$ from the dipole is $$r,$$ (much larger than the size of the dipole) then electric field at $$Q$$ is proportional to

Solution :
Electric field due to a dipole at bisector or at a point on its broad side on position or equatorial position is given by $$E = \frac{1}{{4\pi {\varepsilon _0}}} \cdot \frac{p}{{{r^3}}}$$
or $$E \propto \frac{p}{{{r^3}}}\,......\left( {\text{i}} \right)$$
where, $$r$$ is the distance of that point from centre of dipole and $$p$$ is dipole moment.
So, from Eq. (i)
$$E \propto p\,\,{\text{and}}\,\,E \propto {r^{ - 3}}$$