Identify the correct statements among the following
A. The magnetic field at the center of a coil of radius \(r\) having one turn and carrying current \(I\), is \(\mu_0 I/2r\).
B. The magnetic field produced by a current carrying coil will be parallel to its plane.
C. Magnetic fields produced by two concentric coils of radii \(r_1\) and \(r_2\), in the same plane, having currents \(I_1\) and \(I_2\), respectively, in the same direction, will add up to \(\mu_0 I_1/2r_1 + \mu_0 I_2/2r_2\).
D. The magnetic field produced by a current carrying coil will be perpendicular to its plane along the axis at its center.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, C and D only
At the centre of a circular coil every current element gives a field along the axis (Biot–Savart law):
\( \displaystyle B = \frac{\mu_0 I}{2r} \)
(A) The magnetic field at the center of a coil of radius \( r \) having one turn and carrying current \( I \), is \( \mu_0 I/2r \). — Correct. The standard result above.
(B) The magnetic field produced by a current carrying coil will be parallel to its plane. — Incorrect. The field is perpendicular to the plane of the coil.
(C) Magnetic fields produced by two concentric coils of radii \( r_1 \) and \( r_2 \), in the same plane, having currents \( I_1 \) and \( I_2 \), respectively, in the same direction, will add up to \( \mu_0 I_1/2r_1 + \mu_0 I_2/2r_2 \). — Correct. Both lie along the axis in the same direction, so they add.
(D) The magnetic field produced by a current carrying coil will be perpendicular to its plane along the axis at its center. — Correct. By the right-hand thumb rule.
NCERT (2026-27):
Magnetic Field on the Axis of a Circular Current Loop – “… As a special case of the above result, we may obtain the field at the centre of the loop. Here x = 0, and we obtain,
\( \displaystyle \mathbf{B}_0 = \frac{\mu_0 I}{2R}\,\hat{\mathbf{i}} \qquad (4.12) \)”
Circular Current Loop as a Magnetic Dipole – “… The magnitude of this field is [(Eq. (4.11)],
\( \displaystyle B = \frac{\mu_0 I R^2}{2\left(x^2 + R^2\right)^{3/2}} \)
and its direction is along the axis and given by the right-hand thumb rule (Fig. 4.10).”
Sources and Fields – “… Experimentally, it is found to obey the principle of superposition: the magnetic field of several sources is the vector addition of magnetic field of each individual source.”