To solve this problem, we need to find the electric field intensity at a distance $R$ from a dipole.$\\$Given:$\\$• Two point charges $-q$ and $+q$ separated by a distance $L. \\$• Distance $R$ is much larger than $L$ ($R >> L$).$\\$The electric field due to a dipole at a point on the axial line is given by:$\\ E = \frac{1}{4\pi\varepsilon_0} \cdot \frac{2p}{R^3} \\$where $p$ is the dipole moment, defined as $p = q \cdot L. \\$Since $R >> L,$ the dipole approximation is valid.$\\$Substitute $p = q \cdot L$ into the equation:$\\ E = \frac{1}{4\pi\varepsilon_0} \cdot \frac{2(q \cdot L)}{R^3} \\$This shows that the electric field intensity varies as $\frac{1}{R^3}. \\$Therefore, the correct option is $$Option 2: $\frac{1}{R^3}.$