Question

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

• 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

Answer 1

Answer: (C)

directly proportional to r in the region r < a and inversely proportional to r in the region r > a

Answer 2

It is a case of solid infinite current carrying wire.
Using ampere circuital law,
CASE I: if r ≤ R 𝐵 = 𝜇_0𝑖/2𝜋𝑅^2 𝑟
CASE II: r>R 𝐵 = 𝜇0𝑖 /2𝜋r