Question

The electric field due to a dipole along the line passing through its midpoint and perpendicular to its axis is proportional to

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

Hint:

For an electric dipole, the field decreases rapidly with distance: - Both axial and equatorial fields $\propto \frac{1}{r^3}$.

Answer 1

The Correct Option is B

Concept: An electric dipole produces different electric fields along different directions:
• Along axial line: $E \propto \frac{1}{r^3}$
• Along equatorial line (perpendicular bisector): $E \propto \frac{1}{r^3}$ Thus, in both cases, the electric field varies inversely as the cube of the distance.

Step 1: Identify the given situation.
The question refers to the line:
• Passing through midpoint
• Perpendicular to dipole axis This is the equatorial line of the dipole.

Step 2: Use formula for electric field on equatorial line.
\[ E = \frac{1}{4\pi \epsilon_0} \cdot \frac{p}{r^3} \] where $p$ is dipole moment.

Step 3: Determine proportionality.
\[ E \propto \frac{1}{r^3} \]

Step 4: Final conclusion.
Hence, the electric field varies as: \[ \frac{1}{r^3} \]