A long straight solid cylindrical conductor of radius R carries a steady current I uniformly distributed across its cross-section. Which of the following descriptions correctly represents the variation of the magnetic field magnitude B with radial distance r from the axis of the conductor?

Step-by-step solution

For a long solid cylindrical conductor with a uniform current distribution, we apply Ampere's law. Inside the conductor ( r B d l = ₀ I_ enclosed B(2 r) = ₀ ( I R^2 ) r^2 B = ₀ I r 2 R^2 Thus, B r , which represents a straight line passing through the origin. Outside the conductor ( r > R ): B(2 r) = ₀ I B = ₀ I 2 r Thus, B 1 r , which represents a rectangular hyperbola. Therefore, the magnetic field increases linearly from the axis to the surface, and then decreases hyperbolically outside the conductor. Answer: A