The magnetic field B at a distance r from a long, thin straight wire…

The correct answer is Option (2) → the diagram in Option (2)

By Ampere’s circuital law, the magnetic field at a distance \( r \) from a long straight wire carrying current \( I \) is

    \( \displaystyle B=\frac{\mu_0 I}{2\pi r} \)

so for a steady current \( B \) is inversely proportional to the distance from the wire.

Option (1) — Incorrect. From the figure, \( B \) rises in a straight line through the origin, so \( B\propto r \). This would make the field grow stronger far from the wire, while the field of a wire weakens with distance.

Option (2) — Correct. From the figure, \( B \) is very large close to the wire and falls steadily towards zero as \( r \) increases. This is the curve of \( B\propto1/r \).

Option (3) — Incorrect. From the figure, \( B \) starts at zero and grows with \( r \) before levelling off. The field of a wire does the opposite: it is largest near the wire and decreases with distance.

Option (4) — Incorrect. From the figure, \( B \) first rises in proportion to \( r \) and then falls as \( 1/r \). This is the field of a thick wire, which grows with \( r \) inside the wire; for a thin wire only the falling \( 1/r \) part remains.

NCERT (2026-27):
Ampere’s Circuital Law – “… We find that the magnetic field at a distance r outside the wire is tangential and given by

    \( B\times2\pi r=\mu_0 I, \)

    \( B=\mu_0 I/(2\pi r) \qquad (4.14) \)

… The field is directly proportional to the current and inversely proportional to the distance from the (infinitely long) current source.”