A planar loop of area \(A\) carries a steady current \(I\). Consider the following statements:
(A) At large distances, the loop behaves like a magnetic dipole of moment \(m = IA\).
(B) At a large distance \(x\) on its axis, the magnetic field of the loop varies as \(1/x^{2}\).
(C) At large distances, the magnetic field of the loop is very similar to the electric field of an electric dipole.
(D) Isolated magnetic poles (magnetic monopoles), like electric charges, are known to exist.
Which of the above statements are correct?
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (C) only
Far from a current loop, its field has the same form as the field of an electric dipole. For this reason a current loop is treated as a magnetic dipole.
(A) At large distances, the loop behaves like a magnetic dipole of moment \( m=IA \). — True. Any planar loop is equivalent to a magnetic dipole with \( m=IA \).
(B) At a large distance \( x \) on its axis, the magnetic field of the loop varies as \( 1/x^{2} \). — False. Far from the loop, the axial field is \( \mu_0 2m/4\pi x^{3} \), so it varies as \( 1/x^{3} \).
(C) At large distances, the magnetic field of the loop is very similar to the electric field of an electric dipole. — True. Replacing \( \mu_0 \) by \( 1/\varepsilon_0 \) and \( m \) by \( p_e \) turns the loop’s field into the field of an electric dipole.
(D) Isolated magnetic poles (magnetic monopoles), like electric charges, are known to exist. — False. A magnetic dipole (a current loop) is the most elementary magnetic unit. Magnetic monopoles are not known to exist.
NCERT (2026-27):
Circular current loop as a magnetic dipole – “… a planar current loop is equivalent to a magnetic dipole of dipole moment m = I A, which is the analogue of electric dipole moment p.”
Circular current loop as a magnetic dipole – “As earlier, we define the magnetic moment m to have a magnitude IA, m = I A. Hence,”
\( B\simeq\frac{\mu_0}{4\pi}\frac{2m}{x^{3}} \)\( \qquad [4.25(a)] \)
Circular current loop as a magnetic dipole – “… We shall show that the magnetic field (at large distances) due to current in a circular current loop is very similar in behaviour to the electric field of an electric dipole.”
Circular current loop as a magnetic dipole – “… The equivalent of electric charges, i.e., magnetic monopoles, are not known to exist.”