Biot-Savart law indicates that the moving electrons (velocity \( \vec{v} \)) produce a magnetic field \( \vec{B} \) such that:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \vec{B} \perp \vec{v} \)
By the Biot-Savart law, a charge \( q \) moving with velocity \( \vec{v} \) produces at a point at position \( \vec{r} \) from it the field
\( \displaystyle \vec{B} = \frac{\mu_0}{4\pi}\,\frac{q\,(\vec{v}\times\vec{r})}{r^{3}} \)
The field is a cross product of \( \vec{v} \) and \( \vec{r} \), so it is perpendicular to both of them. Its magnitude is \( \frac{\mu_0}{4\pi}\,\frac{q v \sin\theta}{r^{2}} \), an inverse-square dependence.
Option (1) \( \vec{B} \perp \vec{v} \) — Correct. \( \vec{B} \) is along \( \vec{v}\times\vec{r} \), so it is perpendicular to \( \vec{v} \).
Option (2) \( \vec{B} \parallel \vec{v} \) — Incorrect. A cross product is never parallel to either factor; along the line of motion the field is zero.
Option (3) It obeys inverse cube law — Incorrect. One power of \( r \) in \( r^{3} \) cancels the length of \( \vec{r} \) in the numerator, so the magnitude falls as \( 1/r^{2} \): an inverse-square law.
Option (4) It is along line joining the electron and point of observation — Incorrect. The field is perpendicular to \( \vec{r} \), the line joining the electron and the point, not along it.
Note: A similar question was also asked in CUET (UG) 2026 on 29-05-2026 (Slot 2).
NCERT (2026-27):
Magnetic Field Due to a Current Element, Biot-Savart Law – “… According to Biot-Savart’s law, the magnitude of the magnetic field dB is proportional to the current I, the element length |dl|, and inversely proportional to the square of the distance r. Its direction is perpendicular to the plane containing dl and r.”