Answer:
The electric field due to a point charge q at distance r from it is given by \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{{{r}^{2}}}\] Clearly, the magnitude of field \[\vec{E}\] will be same at all points on the surface of a sphere of radius r drawn around the point charge and does not depend on the direction of\[\vec{r}\] . Hence the field due to a point charge is spherically symmetric. Electric field at distance r on the equatorial line of an electric dipole of dipole moment p is given by \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{p}{{{({{r}^{2}}+{{a}^{2}})}^{3/2}}}\] The electric field E is same at all points which lie on a cylinder of radius r with its axis on the dipole axis and the field pattern looks same in all planes passing through the dipole axis. We say that the electric field of an electric dipole is cylindrically symmetric.
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