A short electric dipole produces an electric field of magnitude \(E_0\) at a point on its axis, at a distance \(r\) from its centre. The distance \(r\) is much larger than the length of the dipole.
Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) Point on the axis at distance \(2r\) | (I) \(E_0/4\) |
| (B) Point on the equatorial plane at distance \(r\) | (II) \(E_0/2\) |
| (C) Point on the axis at distance \(r\), with each charge halved and the distance between the charges halved | (III) \(E_0/8\) |
| (D) Point on the equatorial plane at distance \(r\), with the dipole moment doubled | (IV) \(E_0\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
Far from a dipole, the field on the axis is \( 2p/4\pi\varepsilon_0r^3 \) and the field on the equatorial plane is \( p/4\pi\varepsilon_0r^3 \). Both vary as \( p/r^3 \). At the same distance, the equatorial field is half the axial field. Here \( E_0=2p/4\pi\varepsilon_0r^3 \).
(A) Point on the axis at distance \( 2r \) — This matches (III) \( E_0/8 \). Doubling the distance divides the field by \( 2^3=8 \).
(B) Point on the equatorial plane at distance \( r \) — This matches (II) \( E_0/2 \). At the same distance, the equatorial field is half the axial field.
(C) Point on the axis at distance \( r \), with each charge halved and the distance between the charges halved — This matches (I) \( E_0/4 \). The dipole moment \( p=q\times2a \) becomes \( (q/2)\times a=p/4 \). The field is proportional to \( p \), so it becomes \( E_0/4 \).
(D) Point on the equatorial plane at distance \( r \), with the dipole moment doubled — This matches (IV) \( E_0 \). The field is proportional to \( p \), so \( E_0/2 \) becomes \( E_0 \).
NCERT (2026-27):
The field of an electric dipole – “… In terms of p, the electric field of a dipole at large distances takes simple forms: At a point on the dipole axis”
\( \displaystyle E=\frac{2p}{4\pi\varepsilon_0r^3} \)\( \quad (r\gg a) \)
“At a point on the equatorial plane”
\( \displaystyle E=-\frac{p}{4\pi\varepsilon_0r^3} \)\( \quad (r\gg a) \)
The field of an electric dipole – “… that is, it is a vector whose magnitude is charge q times the separation 2a (between the pair of charges q, –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. …”