Question

The electric potential at a point on the axis of an electric dipole at a distance r from its centre is proportional to

• A. $r$
• B. $1/r$
• C. $1/r^{2}$
• D. $1/r^{3}$
• E. $r^{2}$

Hint:

Contrast this with a single point charge, where potential $V \propto 1/r$. Because a dipole has equal and opposite charges that nearly cancel each other out, its potential drops off much faster than a single charge as you move away.

Answer 1

The Correct Option is C

Concept:
Physics - Electric Potential of a Dipole.
Step 1: State the formula for dipole potential.
For a dipole with dipole moment $p$, the electric potential $V$ at a distance $r$ from the centre (where $r \gg a$) is: $$ V = \frac{kp\cos\theta}{r^2} $$ where $\theta$ is the angle between the position vector and the dipole moment.
Step 2: Apply the condition for the axis.
On the axial line of the dipole, $\theta = 0^{\circ}$ or $180^{\circ}$. $$ \cos(0^{\circ}) = 1 \implies V_{axial} = \frac{kp}{r^2} $$
Step 3: Determine the proportionality.
From the axial potential formula, we can see: $$ V \propto \frac{1}{r^2} $$