For a short electric dipole (dipole length ‘a’) of dipole moment P, match List-I with List-II
| List-I | List-II |
| (A) Potential energy of an electric dipole placed in a uniform electric field. | (I) \( E = \displaystyle\frac{2P}{4\pi\epsilon_0 r^{3}} \) |
| (B) Electric potential on the equatorial plane of the dipole. | (II) \( \displaystyle\frac{2q}{\pi\epsilon_0 a^{2}} \) |
| (C) Magnitude of electric field intensity at mid-point of a dipole | (III) \( -(\vec{P}.\vec{E}) \) |
| (D) Magnitude of electric field intensity on the axial line from the center of the dipole | (IV) 0 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (III), (B) - (IV), (C) - (II), (D) - (I)
A dipole consists of charges +q and −q a distance a apart, with dipole moment P = qa.
(A) Potential energy of an electric dipole placed in a uniform electric field. — this matches (III) \( -(\vec{P}.\vec{E}) \), i.e. \( U = -PE\cos\theta \).
(B) Electric potential on the equatorial plane of the dipole. — this matches (IV) 0. Every point of it is equidistant from +q and −q, so their potentials cancel.
(C) Magnitude of electric field intensity at mid-point of a dipole — this matches (II) \( 2q/\pi\epsilon_0 a^{2} \). Each charge is a/2 away and both fields point from +q towards −q, so they add.
\( \displaystyle E = 2 \times \frac{1}{4\pi\epsilon_0}\frac{q}{(a/2)^{2}} \)
\( \displaystyle E = \frac{8q}{4\pi\epsilon_0 a^{2}} = \frac{2q}{\pi\epsilon_0 a^{2}} \)
(D) Magnitude of electric field intensity on the axial line from the center of the dipole — this matches (I) \( E = 2P/4\pi\epsilon_0 r^{3} \), the axial field of a short dipole at a distance r (r much greater than a).
Note: It seems that there is a mistake in the original NTA paper, which prints (D) without any distance, though entry (I) uses r. The question can still be solved, because (I) is the only entry that has the form of the axial field of a short dipole.