Question

Write down the formula for the electric potential on the axial line of an electric dipole.

Hint:

On axial line: $V = \dfrac{p}{4\pi\epsilon_0 r^2}$, On equatorial line: $V = 0$ (due to symmetry).

Answer 1

Step 1: Recall definition of dipole.
A dipole consists of charges $+q$ and $-q$ separated by distance $2a$. Dipole moment $p = q \cdot 2a$.
Step 2: Potential on axial line.
At a point $P$ at distance $r$ from the center on the axial line: \[ V = \frac{1}{4\pi\epsilon_0} \cdot \frac{p}{r^2}. \]
Step 3: Conclusion.
Thus, the potential decreases as $\dfrac{1}{r^2}$.