According to the Biot-Savart law, the magnetic field due to a current…

The correct answer is Option (2) → (A), (B) and (C) only

The Biot-Savart law gives the field of a current element \( I\,d\vec{l} \) at a point with position vector \( \vec{r} \) from the element:

    \( \displaystyle d\vec{B} = \frac{\mu_0}{4\pi}\,\frac{I\,d\vec{l}\times\vec{r}}{r^{3}}, \qquad |d\vec{B}| = \frac{\mu_0}{4\pi}\,\frac{I\,dl\,\sin\theta}{r^{2}} \)

(A) inversely proportional to the square of the distance from the current element to the point of interest. — Correct. \( |d\vec{B}| \propto 1/r^{2} \).

(B) produced by a vector source. — Correct. The source \( I\,d\vec{l} \) is a vector: it has a magnitude and the direction of the current.

(C) perpendicular to the plane containing the displacement vector and the current element. — Correct. Being a cross product, \( d\vec{B} \) is perpendicular to both \( d\vec{l} \) and \( \vec{r} \).

(D) non-zero at any point in the direction of the current element. — Incorrect. Along the direction of the element \( \theta = 0^\circ \), so \( \sin\theta = 0 \) and \( d\vec{B} = 0 \).

Statements (A), (B) and (C) are correct, which is Option (2).

NCERT (2026-27):
Magnetic Field Due to a Current – “… (i) Both are long range, since both depend inversely on the square of distance from the source to the point of interest.”

Magnetic Field Due to a Current – “… (ii) … The magnetic field is produced by a vector source \( I\,d\mathbf{l} \).”

Magnetic Field Due to a Current – “… (iii) … The magnetic field is perpendicular to the plane containing the displacement vector \( \mathbf{r} \) and the current element \( I\,d\mathbf{l} \).”

Magnetic Field Due to a Current – “… (iv) There is an angle dependence in the Biot-Savart law which is not present in the electrostatic case. In Fig. 4.7, the magnetic field at any point in the direction of \( d\mathbf{l} \) (the dashed line) is zero.”