Read the following passage and answer the questions.
A student studies the magnetic field produced by a steady current. She uses the Biot-Savart law. First she takes a short straight piece of wire, 1 cm long, placed at the origin. It carries a current of 5 A in the +x direction. She marks some points, each 10 cm from this piece. Some of these points lie on the x-, y- and z-axes. One point, Q, lies in the x-y plane, on a line that makes an angle of 30° with the +x-axis. She also moves a point P along the +y-axis to see how the field changes with distance. Next, she bends a long wire into a flat circular loop of radius \(R\) and passes a steady current \(I\) through it. She treats the loop as a large number of small current elements. She then studies the field at the centre of the loop and at points on its axis.
Point P is moved along the +y-axis, away from the piece of wire. The magnitude of the field at P is plotted against \(1/r^{2}\), where \(r\) is the distance of P from the piece. The graph is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → a straight line passing through the origin
On the +y-axis the angle between the wire piece and the line to P stays 90°. So only the distance \( r \) changes. The Biot-Savart law gives \( dB\propto 1/r^{2} \) for a fixed current element and a fixed angle.
Option (1) a straight line with a negative slope — Incorrect. The field falls as P moves away, but a graph against \( 1/r^{2} \) is not a falling line. A larger value of \( 1/r^{2} \) means P is closer, so the field is larger.
Option (2) a curve that bends towards the \(1/r^{2}\) axis — Incorrect. Such a curve would come from \( dB\propto 1/r \), the law for a long straight wire. A short piece of wire follows the inverse square law.
Option (3) a straight line passing through the origin — Correct. Since \( dB=k\,(1/r^{2}) \) with \( k=\mu_0I\,dl/4\pi \), the graph is a straight line of slope \( k \). The field becomes zero when \( 1/r^{2} \) becomes zero, so the line passes through the origin.
Option (4) a straight line parallel to the \(1/r^{2}\) axis — Incorrect. A line parallel to the axis means the field does not change with distance. The field of a current element does depend on \( r \).
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. …”