Intensity of an electric field (E) depends on distance r, due to a dipole, is related as ?

Intensity of an electric field (E) depends on distance r, due to a dipole, is related as ?

(a) \( E \propto \frac{1}{r} \)

(b) \( E \propto \frac{1}{r^2} \)

(c) \( E \propto \frac{1}{r^3} \)

(d) \( E \propto \frac{1}{r^4} \)

Answer :  (c) \( E \propto \frac{1}{r^3} \)

\( E = \frac{-1}{4 \pi \varepsilon_0} \cdot \frac{\vec{p}}{r^3} \)

\( l \ll r \)

\( E_{\text{mid}} = k \cdot \frac{2\vec{p}}{r^3} \)

\( E_{\text{axial}} = k \cdot \frac{2 p r}{(r^2 - l^2)^2} \)

\( E_{\text{eq}} = k \cdot \frac{p r}{(r^2 + l^2)^{3/2}} \)

\( E \propto \frac{1}{r^3} \)