Question

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

• A. Zero in the region \( r<a \) and inversely proportional to \( r \) in the region \( r>a \)
• B. Inversely proportional to \( r \) in the region \( r<a \) and uniform throughout in the region \( r>a \)
• C. Directly proportional to \( r \) in the region \( r<a \) and inversely proportional to \( r \) in the region \( r>a \)
• D. Uniform in the region \( r<a \) and inversely proportional to distance \( r \) from the axis, in the region \( r>a \)

Hint:

For a long straight wire with uniformly distributed current:
Inside the wire (\( r<a \)), \( B \propto r \).
Outside the wire (\( r>a \)), \( B \propto \frac{1}{r} \).