According to the Biot- Savart law, the magnetic field due to a current element is
(A) inversely proportional to the square of the distance from the current element to the point of interest.
(B) produced by a vector source.
(C) perpendicular to the plane containing the displacement vector and the current element.
(D) non-zero at any point in the direction of the current element.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (C) only
According to Biot–Savart law, the magnetic field at a point due to a small current element is given by:
$dB = \frac{\mu_0}{4\pi} \cdot \frac{I \, dl \, \sin\theta}{r^2}$
Where:
$I$ = current in the conductor
$dl$ = infinitesimal length element in the direction of current
$r$ = distance from the current element to the point of observation
$\theta$ = angle between the current element and the position vector
From the above formula:
(A) Correct — Magnetic field is proportional to $\frac{1}{r^2}$,.
(B) Correct — The term $Idl$ is a vector, so the source of the magnetic field is a vector quantity.
(C) Correct — Since the formula involves a cross product, the magnetic field is perpendicular to the plane containing $dl$ and $r$.
(D) Incorrect — When the point lies along the direction of the current ($\theta = 0^\circ$), $\sin\theta = 0$, hence $dB = 0$.