For a short electric dipole, identify the incorrect statement(s).
(A) The electric field intensity varies inversely with the cube of the distance from the center of the dipole.
(B) The electric field is directed from negative to positive charge.
(C) The electric potential at mid-point of the dipole is zero.
(D) The electric field intensity at mid-point of the dipole is zero.
Choose the correct answer from the option given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) and (D) only
The question asks for the incorrect statements, so each statement is marked as a correct or an incorrect statement about the dipole. Let the dipole have charges \( +q \) and \( -q \) a distance \( 2a \) apart.
(A) The electric field intensity varies inversely with the cube of the distance from the center of the dipole. — Correct. For a short dipole the field far away is \( E \propto 1/r^{3} \), since the fields of the two charges almost cancel.
(B) The electric field is directed from negative to positive charge. — Incorrect. The field lines of a dipole start on the positive charge and end on the negative charge, so the field is directed from positive to negative charge.
(C) The electric potential at mid-point of the dipole is zero. — Correct. The potentials of \( +q \) and \( -q \) at equal distances are \( +kq/a \) and \( -kq/a \), and they cancel.
(D) The electric field intensity at mid-point of the dipole is zero. — Incorrect. At the mid-point the fields of the two charges point the same way, from \( +q \) towards \( -q \), and add.
\( \displaystyle E = \frac{kq}{a^{2}} + \frac{kq}{a^{2}} = \frac{2kq}{a^{2}} \neq 0 \)
So the incorrect statements are (B) and (D).
NCERT (2026-27):
The Field of an Electric Dipole – “… Notice the important point that the dipole field at large distances falls off not as \( 1/r^2 \) but as \( 1/r^3 \).”
Potential Due to an Electric Dipole – “… The potential in the equatorial plane (\( \theta = \pi/2 \)) is zero.”