Question

The electrostatic energy of the system made by two electric dipoles kept at a distance \( r \) is proportional to:

• A. \( r^2 \)
• B. \( r^3 \)
• C. \( r^4 \)
• D. none of these

Hint:

Remember: The interaction energy between two dipoles varies as \( 1/r^3 \).

Answer 1

The Correct Option is B

The potential energy \( U \) between two electric dipoles separated by a distance \( r \) varies inversely as the cube of the distance between them. Mathematically, this is expressed as: \[ U \propto \frac{1}{r^3}. \] This relationship arises from the interaction between the dipole moments and the electric fields produced by each dipole. The derivation involves vector calculus and the superposition principle, but the key takeaway is the inverse cubic dependence. None of the given options explicitly show an inverse power relationship. However, the closest match is option (B) if it is interpreted as implying an inverse cube dependence. Therefore, based on the nature of dipole-dipole interactions, the correct or most appropriate choice is option (B).