Identify the incorrect statement(s) among the following.
(A) Two electric field lines of forces never intersect each other.
(B) Two opposite charges, each of \( 10\times10^{-9}\,\mathrm{C} \), are separated by a distance of 5 mm. The magnitude of the dipole moment is \( 5\times10^{-11}\,\mathrm{C\,m} \).
(C) Electric field intensity at a point due to a single charge varies inversely as the square of the distance from the charge, whereas electric field intensity due to an electric dipole varies inversely as the cube of the distance of the point.
(D) Electric field intensity due to an electric dipole has a spherical symmetry around it in space.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (D) only
(A) Two electric field lines of forces never intersect each other. — True statement. At a point of intersection the field would have two directions, which is impossible.
(B) Two opposite charges, each of \( 10\times10^{-9}\,\mathrm{C} \), are separated by a distance of 5 mm. The magnitude of the dipole moment is \( 5\times10^{-11}\,\mathrm{C\,m} \). — True statement. The dipole moment is charge times separation.
\( \displaystyle p = q \times 2a = 10\times10^{-9} \times 5\times10^{-3} = 5\times10^{-11}\,\mathrm{C\,m} \)
(C) Electric field intensity at a point due to a single charge varies inversely as the square of the distance from the charge, whereas electric field intensity due to an electric dipole varies inversely as the cube of the distance of the point. — True statement. The field of a dipole falls faster than that of a single charge because the two opposite fields partly cancel at large distance.
(D) Electric field intensity due to an electric dipole has a spherical symmetry around it in space. — False statement. A dipole has a definite axis: its field on the axis is twice that on the equatorial line at the same distance. Only a single point charge has a spherically symmetric field.
NCERT (2026-27):
Electric Field Lines – “… (iii) Two field lines can never cross each other.”
Summary – “… Its dipole moment vector p has magnitude 2qa and is in the direction of the dipole axis from –q to q.”
The Field of an Electric Dipole – “… Notice the important point that the dipole field at large distances falls off not as 1/r2 but as 1/r3. Further, the magnitude and the direction of the dipole field depends not only on the distance r but also on the angle between the position vector r and the dipole moment p.”