According to Ampère’s circuital law, how does magnetic field B vary with radial distance r inside and outside a long straight conductor of circular cross-section, carrying uniform steady current?
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According to Ampère’s circuital law, how does magnetic field B vary with radial distance r inside and outside a long straight conductor of circular cross-section, carrying uniform steady current?

G1 Physics · Accepted Answer

Step 1: For a long conductor of radius R with uniformly distributed current I, current enclosed within radius r<R is I(enclosed)=I(r²/R²). Step 2: Ampère's law B(2πr)=μ₀I(enclosed) yields B=μ₀Ir/(2πR²) for r<R. Step 3: Outside, enclosed current is full I, giving B=μ₀I/(2πr). Thus B rises linearly inside and decreases as 1/r outside. Option C. Final answer: (C) B increases linearly with r inside and decreases as 1/r outside..