The magnetic field due to a straight infinite current carrying wire has
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → cylindrical symmetry
The field of a long straight wire has magnitude \( B = \mu_0 I/2\pi r \) and its field lines are concentric circles around the wire, in planes perpendicular to it.
\( \displaystyle B = \frac{\mu_0 I}{2\pi r} \)
B depends only on the perpendicular distance r from the wire. So the field looks the same after any rotation about the wire and any shift along it, which is cylindrical symmetry; this is what makes Ampère’s circuital law easy to apply with a circular loop around the wire.
Why the other options are incorrect
Option (2) spherical symmetry — Incorrect. Spherical symmetry belongs to the field of a point charge or a spherical charge distribution, which depends only on the distance from a point.
Option (3) elliptical symmetry — Incorrect. The field lines are circles, not ellipses, and B is the same at every point of each circle.
Option (4) parabolic symmetry — Incorrect. Nothing in the field of a straight wire has a parabolic form.
NCERT (2026-27):
Ampere’s Circuital Law – “… (i) It implies that the field at every point on a circle of radius \( r \), (with the wire along the axis), is same in magnitude. In other words, the magnetic field possesses what is called a cylindrical symmetry.”