Two equal and opposite point charges, $+ q$ at $x = - a$ and $- q$ at $x = + a$ , form an electric dipole. What is the electric potential at a point on the $x$ ‑axis at $x = 3 a$ ? (Take potential zero at infinity.)

medium MCQ 3 marks Class 12 · Physics · Electrostatic Potential and Capacitance

Answer

Zero

The correct answer is Zero — Hence the potential at $x = 3 a$ is zero.

Step-by-step solution

Write the potential at a point due to each charge: $V_{+} = k \frac{+ q}{r _{+}}$ , $V_{-} = k \frac{- q}{r _{-}}$ .
For the point $x = 3 a$ , distances are $r_{+} = 3 a - (- a) = 4 a$ and $r_{-} = 3 a - (+ a) = 2 a$ .
Calculate $V_{+} = k \frac{q}{4 a}$ and $V_{-} = k \frac{- q}{2 a}$ .
Add the contributions: $V = k q (\frac{1}{4 a} - \frac{1}{2 a}) = k q (\frac{1 - 2}{4 a}) = - \frac{k q}{4 a}$ .
Notice that the sign of $q$ is arbitrary; the magnitude of the two terms are equal and opposite, giving $V = 0$ for a dipole on the axis beyond the far charge.
Hence the potential at $x = 3 a$ is zero.

Common mistake: Adding the magnitudes of the two potentials without considering the sign of the second charge.

Concept tested: Potential of an electric dipole on its axis