Question

The electrostatic potential due to an electric dipole at a distance \( r \) varies as:

• A. \( r \)
• B. \( \frac{1}{r^2} \)
• C. \( \frac{1}{r^3} \)
• D. \( \frac{1}{r} \)

Hint:

The electric potential due to a monopole (point charge) follows a \( \frac{1}{r} \) relationship, whereas for a dipole, the potential decreases with the square of the distance, \( \frac{1}{r^2} \).

Answer 1

The Correct Option is B

The electrostatic potential \( V_p \) at a point at distance \( r \) from the center of an electric dipole is inversely proportional to the square of the distance: \[ V_p \propto \frac{1}{r^2}. \] This is because the potential due to a dipole decreases at a faster rate compared to a point charge, which follows the \( \frac{1}{r} \) dependence. In a dipole, the opposing charges create a field that reduces more sharply with distance. Final Answer: \[ \boxed{\frac{1}{r^2}}. \]