Question

Two point charges -q and +q are placed at a distance of L, as shown in the figure.

The magnitude of electric field intensity at a distance R (R>>L) varies as:

• A. \(\frac{1}{R^2}\)
• B. \(\frac{1}{R^3}\)
• C. \(\frac{1}{R^4}\)
• D. \(\frac{1}{R^6}\)

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Two equal and opposite charges separated by a small distance constitute an electric dipole.
The electric field of a single point charge varies as \(1/R^2\). However, for a dipole, the fields from the two charges partially cancel out at large distances, leading to a faster rate of decrease.
Key Formula or Approach:
For a dipole of moment \(\vec{p} = q\vec{L}\):
1. Electric field on the axial line (\(E_{axial}\)) \(\approx \frac{2kp}{R^3}\) for \(R >> L\).
2. Electric field on the equatorial line (\(E_{eq}\)) \(\approx \frac{kp}{R^3}\) for \(R >> L\).
Step 2: Detailed Explanation:
In both cases (axial and equatorial), the electric field intensity \(E\) is inversely proportional to the cube of the distance from the center of the dipole.
Mathematically, for any point at a large distance \(R\) from the center of the dipole:
\[ E \propto \frac{1}{R^3} \]
This is a general property of dipole fields in the "far-field" approximation (\(R >> L\)).
Step 3: Final Answer:
The magnitude of electric field intensity varies as \(\frac{1}{R^3}\).