Magnetic field direction around a long, straight current-carrying wire A long, straight wire carries current I. What is the direction of the magnetic field intensity H at a point located a distance r from the wire?

Introduction / Context:The magnetic field around a long straight conductor is a classic result from Ampère’s law and the right-hand rule. Recognizing its circular symmetry is essential for field calculations and for interpreting forces on nearby conductors and magnetic materials.

Given Data / Assumptions:

• Infinite (or sufficiently long) straight wire carrying steady current I.
• Point of observation at distance r from the wire in free space.
• Quasi-static conditions; displacement current negligible.

Concept / Approach:

By symmetry, magnetic field lines form concentric circles around the wire. The magnitude is given by Ampère’s law: H = I/(2π r) (in A/m) and B = μ0 H. The field direction is tangential to these circles, with sense given by the right-hand rule (thumb along current, fingers curl in direction of H/B).

Step-by-Step Solution:

Verification / Alternative check:

Field mapping experiments with iron filings or magnetic compasses around a straight conductor show circular patterns, confirming the theory.

Why Other Options Are Wrong:

(a) and (b) imply radial fields which do not satisfy ∇·B = 0 and symmetry; (d) is along the wire, incorrect; (e) is false since field extends into space around the wire.

Common Pitfalls:

Mixing electric field lines (radial from a charged wire) with magnetic field lines (circular around a current); forgetting the 1/r decay of magnitude.

Final Answer:

Tangential everywhere to a circle of radius r centered on the wire