Question

The electric field intensity due to an ideal dipole at a distance \( r \) from its center on the axial point is directly proportional to:

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

Hint:

The electric field intensity due to a dipole at an axial point decreases with the cube of the distance from the dipole, which is represented by \( \frac{1}{r^3} \).

Answer 1

Answer: (E)

The electric field intensity \( E \) due to an ideal dipole at a distance \( r \) from its center on the axial point is given by the following formula: \[ E = \frac{1}{4 \pi \varepsilon_0} \cdot \frac{2p}{r^3} \] where: - \( p \) is the dipole moment,
- \( r \) is the distance from the dipole.
From the equation, it is clear that the electric field intensity \( E \) is inversely proportional to \( r^3 \).
Thus, the correct answer is option (E), \( \frac{1}{r^3} \).