Question:
The electric potential at a point on the axis of an electric dipole at a distance r from its center is proportional to:
The electric potential at a point on the axis of an electric dipole at a distance r from its center is proportional to:
Show Hint
Dipole relations:
\[
E \propto \frac{1}{r^3}, \quad V \propto \frac{1}{r^2}
\]
Updated On: Jun 10, 2026
- \( \frac{1}{r} \)
- \( \frac{1}{r^2} \)
- \( \frac{1}{r^3} \)
- \( r^2 \)
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The Correct Option is B
Solution and Explanation
Concept:
For an electric dipole, potential at a point is:
\[
V = \frac{1}{4\pi\varepsilon_0}\frac{p \cos\theta}{r^2}
\]
On axial line, \( \cos\theta = 1 \), so:
\[
V \propto \frac{1}{r^2}
\]
Step 1: Axial point condition For point on axis: \[ V = \frac{1}{4\pi\varepsilon_0}\frac{p}{r^2} \]
Step 2: Proportionality Since \(p\) and constants are fixed: \[ V \propto \frac{1}{r^2} \] Thus: \[ \boxed{\frac{1}{r^2}} \]
Step 1: Axial point condition For point on axis: \[ V = \frac{1}{4\pi\varepsilon_0}\frac{p}{r^2} \]
Step 2: Proportionality Since \(p\) and constants are fixed: \[ V \propto \frac{1}{r^2} \] Thus: \[ \boxed{\frac{1}{r^2}} \]
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