Correct Option: (C) concentric horizontal circles around the wire.
Step 1 (Governing Law & Principle): [1/3 Mark]
According to the Biot-Savart Law and the Right-Hand Thumb Rule, the magnetic field $\vec{B}$ produced by a steady current $I$ flowing through a long straight conductor is directed tangentially to circles centered on the wire. The magnitude of the magnetic field at a perpendicular distance $r$ from the wire is given by:
$$B = \frac{\mu_0 I}{2\pi r}$$Step 2 (Step-by-Step Deduction): [1/3 Mark]
- The current $I$ flows vertically upwards along the axis of the wire.
- By applying the Right-Hand Thumb Rule: If the thumb points in the direction of the current (upwards), the curled fingers represent the direction of the magnetic field lines.
- Since the wire is straight and the field lines must be perpendicular to the direction of current flow at every point, the lines form closed loops in the horizontal plane.
- These loops are equidistant from the wire at any given radius $r$, resulting in a pattern of concentric circles.
Step 3 (Final Concluded Answer): [1/3 Mark]
The magnetic field lines are concentric horizontal circles centered on the wire, lying in a plane perpendicular to the wire. Thus, option (C) is the correct choice.
💡 EL10 Concept Insight: Imagine the wire is a straw and you are looking down at it; the magnetic field lines act like invisible rings wrapped around the straw, getting weaker the further out you go, just like ripples spreading out in a pond.