Question

Electric field intensity due to an electric dipole of very small length at a point on axial line at a distance r from its center varies as:

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

Hint:

For an electric dipole, the field intensity on the axial line falls off as \( r^{-3} \), while for a point charge, it falls off as \( r^{-2} \).

Answer 1

The Correct Option is D

Step 1: Understanding the concept.
For an electric dipole, the electric field at a point on the axial line at a distance \( r \) from the center of the dipole varies with the inverse cube of the distance (\( r^{-3} \)). The field intensity \( E \) due to an electric dipole is given by: \[ E = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{2p}{r^3} \] where \( p \) is the dipole moment and \( r \) is the distance from the center of the dipole along the axial line. This shows that the electric field intensity decreases as \( r^{-3} \). Step 2: Analyzing the options.
(1) \( r \): This is incorrect. The electric field intensity does not vary linearly with distance for a dipole.
(2) \( r^2 \): This is incorrect. This would be true for a point charge, not a dipole.
(3) \( r^{-2} \): This is incorrect. This would apply to the electric field of a monopole or point charge, but not a dipole.
(4) \( r^{-3} \): Correct. The electric field intensity due to a dipole falls off as \( r^{-3} \) along the axial line. Step 3: Conclusion.
The correct answer is (4) \( r^{-3} \), as the electric field due to a dipole decreases with the cube of the distance on the axial line.