Which of the following is a similarity between the Biot-Savart law and Coulomb’s law?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both are long range, since both depend inversely on the square of the distance from the source.
Option (1) The electrostatic field is along the displacement vector joining the source and the field point. — Incorrect. This is a difference between the two laws. The magnetic field of a current element is perpendicular to the plane containing \( I\,d\vec{l} \) and \( \vec{r} \). It does not point along \( \vec{r} \).
Option (2) The Biot-Savart law deals with a vector source. — Incorrect. This too is a difference. The source of the magnetic field is the vector \( I\,d\vec{l} \), while the source of the electrostatic field is the scalar charge.
Option (3) Both are long range, since both depend inversely on the square of the distance from the source. — Correct. The field of a charge falls as \( 1/r^{2} \), and the field of a current element also falls as \( 1/r^{2} \). So both fields are long range and follow an inverse-square law.
Option (4) The Biot-Savart law depends upon the angle between the source element and the line joining it to the field point. — Incorrect. This is also a difference. The \( \sin\theta \) factor in the Biot-Savart law has no match in the electrostatic case. There, the field of a charge has the same magnitude in every direction at a given distance.
NCERT (2026-27):
Magnetic Field Due to a Current Element, Biot-Savart Law – “The Biot-Savart law for the magnetic field has certain similarities, as well as, differences with the Coulomb’s law for the electrostatic field. Some of these are: (i) Both are long range, since both depend inversely on the square of distance from the source to the point of interest. The principle of superposition applies to both fields.”