A long, straight solid conducting wire of radius a carries steady current I uniformly distributed over its cross-section. Which labelled B-versus-r graph correctly shows magnetic field magnitude B versus distance r from the wire axis (inside and outside the wire)? Image
Options

Question

A long, straight solid conducting wire of radius a carries steady current I uniformly distributed over its cross-section. Which labelled B-versus-r graph correctly shows magnetic field magnitude B versus distance r from the wire axis (inside and outside the wire)? Image

Options

G1 Physics · Accepted Answer

Step 1: By Ampère’s law, ∮B·dl = μ₀I(enclosed). Step 2: For r < a, enclosed current I(enclosed) = I(r²/a²). Hence B(2πr) = μ₀I(r²/a²), so B = μ₀Ir/(2πa²) ∝ r. Step 3: For r ≥ a, the enclosed current is I. Therefore B = μ₀I/(2πr) ∝ 1/r. Step 4: Magnetic field increases linearly from zero inside, peaks at the surface r = a, and falls inversely with r outside. Final answer: Graph C (Option C).