A long, straight wire having radius R carries a current which is uniformly distributed across its cross section. The magnitude of the magnetic field produced is

Step-by-step solution

For a long straight wire of radius R carrying a steady current I uniformly distributed across its cross-section, the magnetic field at a distance r from the axis is obtained using Ampere's circuital law. Inside the wire ( r B d l = ₀ I_ enclosed B(2 r) = ₀ ( I R^2 ) r^2 B = ₀ I r 2 R^2 The magnetic field is directly proportional to r . At the axis ( r = 0 ), the magnetic field is zero, which is its minimum magnitude. Outside the wire ( r R ): B d l = ₀ I B(2 r) = ₀ I B = ₀ I 2 r The magnetic field is inversely prop