The electric potential for an electric dipole

The correct answer is Option (3) → is zero at mid-point on the line, joining two charges of dipole

The potential of a dipole is the scalar sum of the potentials of its two charges.

    \( \displaystyle V = \frac{1}{4\pi\varepsilon_0}\left(\frac{q}{r_{+}} - \frac{q}{r_{-}}\right) \)

At the mid-point of the line joining the charges, \( r_{+} = r_{-} \), so the two terms cancel and \( V = 0 \).

Option (1) varies inversely with the distance from the center of the dipole on the equatorial line. — Incorrect. On the equatorial line every point is equidistant from \( +q \) and \( -q \), so the potential is zero everywhere on it; it does not vary as \( 1/r \).

Option (2) is a vector quantity — Incorrect. Potential is a scalar; only the field of the dipole is a vector.

Option (3) is zero at mid-point on the line, joining two charges of dipole — Correct. The mid-point is equidistant from the two equal and opposite charges, so their potentials cancel.

Option (4) has a direction from charge \( -q \) towards \( +q \) — Incorrect. A scalar has no direction; it is the dipole moment that points from \( -q \) to \( +q \).

NCERT (2026-27):
Potential Due to an Electric Dipole – “… The potential in the equatorial plane (\( \theta = \pi/2 \)) is zero.”

Potential Due to an Electric Dipole – “… (ii) The electric dipole potential falls off, at large distance, as 1/r², not as 1/r, characteristic of the potential due to a single charge.”