A thick cable of radius R carries current I uniformly distributed over its cross-section. Which graph correctly represents magnetic field B(r) against distance r from its axis? [Image]
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A thick cable of radius R carries current I uniformly distributed over its cross-section. Which graph correctly represents magnetic field B(r) against distance r from its axis? [Image]

G1 Physics · Accepted Answer

Step 1: For 0 < r < R and uniform current density, enclosed current I_encl = I(r²/R²). Step 2: Apply Ampère's law 2πrB = μ₀I_encl to find B_inside = μ₀Ir/(2πR²), which increases linearly from zero. Step 3: For r ≥ R, enclosed current becomes I and B_outside = μ₀I/(2πr), which decreases as 1/r. Step 4: The correct graph rises linearly to r=R and decays as 1/r outside. Final answer: (C), refer to source diagram / graph.