1. Electric field of a short dipole

For a short electric dipole of dipole moment $p$, the electric field at a point far away from the dipole depends on whether the point lies on the axial line or the equatorial line.

2. Field on the equatorial plane

At a point on the equatorial plane at a large distance $r$ from the center of the dipole, the magnitude of electric field is

Thus,

3. Check options

• A: $\frac{1}{r^2}$ ❌
• B: $\frac{1}{r}$ ❌
• C: $r$ ❌
• D: $\frac{1}{r^3}$ ✅

4. Conclusion

The electric field due to a short electric dipole on the equatorial plane varies inversely as the cube of the distance.