A long straight wire of radius "a" carries a steady current...

A long straight wire of radius "a" carries a steady current I the current is uniformly distributed across its cross-section. The ratio of the magnetic field at $\mathrm{a} / 2$ and $2 \mathrm{a}$ is
(a) $(1 / 4)$
(b) 4
(c) 1
(d) $(1 / 2)$

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Key Concepts

Magnetic Field Distribution in Cylindrical Conductors

For cylindrical conductors carrying a uniformly distributed current, the magnetic field inside (at a radius less than the conductor's radius) increases linearly with distance from the center, while outside the conductor it decreases inversely with distance. This distinction is crucial when determining the magnetic field at different positions relative to the conductor.

Ampere's Law

Ampere's Law is a foundational principle in electromagnetism that relates the integrated magnetic field around a closed loop to the steady current passing through the loop. It is especially useful for calculating magnetic fields in systems with high symmetry, such as a long straight wire, enabling derivations for both the internal and external field distributions.

Uniform Current Density

Uniform current density means that the electric current is spread evenly across the cross-sectional area of a conductor. This uniformity simplifies the analysis of the magnetic field inside the conductor, as the enclosed current for a given radius can be calculated as a fraction of the total current based on the area ratio.

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