Identify the correct statements given below about the magnetic field due to a current element (source).
(A) It is the field produced by a vector source.
(B) It is along the displacement vector joining the source and the field point.
(C) It is dependent on angle between the current element and the displacement vector joining it with the field point.
(D) It is long range.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (C) and (D) only
The field of a current element \( I\,d\vec{l} \) is given by the Biot–Savart law, where \( \vec{r} \) is the displacement vector from the element to the field point and \( \theta \) the angle between them.
\( \displaystyle d\vec{B} = \frac{\mu_0}{4\pi}\,\frac{I\,d\vec{l} \times \vec{r}}{r^{3}} \)
\( \displaystyle dB = \frac{\mu_0}{4\pi}\,\frac{I\,dl\,\sin\theta}{r^{2}} \)
(A) It is the field produced by a vector source. — Correct. The source is the current element \( I\,d\vec{l} \), which has a direction (along the current), unlike a point charge, which is a scalar source.
(B) It is along the displacement vector joining the source and the field point. — Incorrect. \( d\vec{B} \) is along the cross product \( d\vec{l} \times \vec{r} \), so it is perpendicular to the displacement vector (and to the current element).
(C) It is dependent on angle between the current element and the displacement vector joining it with the field point. — Correct. dB contains the factor \( \sin\theta \); it is largest at 90° and zero at points along the line of the element.
(D) It is long range. — Correct. The field falls off as \( 1/r^{2} \), the same inverse-square dependence as the electric field of a point charge, so it extends to large distances.
NCERT (2026-27):
Magnetic Field Due to a Current – “… The Biot-Savart law for the magnetic field has certain similarities, as well as, differences with the Coulomb’s law for the electrostatic field. … (i) Both are long range, since both depend inversely on the square of distance from the source to the point of interest. … (ii) The electrostatic field is produced by a scalar source, namely, the electric charge. The magnetic field is produced by a vector source \( I\,d\mathbf{l} \). (iii) The electrostatic field is along the displacement vector joining the source and the field point. The magnetic field is perpendicular to the plane containing the displacement vector \( \mathbf{r} \) and the current element \( I\,d\mathbf{l} \). (iv) There is an angle dependence in the Biot-Savart law which is not present in the electrostatic case.”