Question

At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as

• A. $\frac{1}{r}$
• B. $\frac{1}{r^2}$
• C. $\frac{1}{r^3}$
• D. $\frac{1}{r^4}$

Hint:

The electric field of a dipole falls off as $1/r^3$, unlike a point charge which falls off as $1/r^2$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For an electric dipole, the electric field falls off faster than that of a point charge.
Step 2: Detailed Explanation:
For a dipole, the electric field at a distance $r$ along the axial line is $E = \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3}$ for $r \gg$ dipole length. Hence, $E \propto \frac{1}{r^3}$.
Step 3: Final Answer:
The electric field varies as $\frac{1}{r^3}$.