A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

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Zero in the region r < a, and inversely proportional to r in the region r > a

Inversely proportional to r in the region r < a, and uniform throughout in the region r > a

Directly proportional to r in the region r < a, and inversely proportional to r in the region r > a

Uniform in the region r < a, and inversely proportional to distance r from the axis, in the region r > a

answer is C.

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Detailed Solution

For

$\begin{array}{l} r < a \\ \int \vec{B} \cdot d \vec{ℓ} = μ_{0} i \\ B . (2 π) = \frac{μ_{0} I}{π a^{2}} \cdot π r^{2} \\ B = \frac{μ_{0} I r}{2 π a^{2}} \end{array}$

$B∝r$

For

$\begin{array}{l} r > a \\ \int \vec{B} \cdot d \vec{ℓ} = μ_{0} I \end{array}$

$\begin{array}{l} B .2 π R = μ_{0} I \\ B = \frac{μ_{0} I}{2 π r} \Rightarrow B \propto \frac{1}{r} \end{array}$

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