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A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances a/2 and 2a respectively, from the axis of the wire is:
- 1 / 4
- 1 / 2
- 1
- 4
Correct answer: 4
Solution
Inside the wire (r = a/2), the magnetic field is proportional to r, so B ∝ (a/2). Outside the wire (r = 2a), the magnetic field is inversely proportional to r, so B' ∝ 1/(2a). The ratio B/B' = (a/2) / (1/(2a)) = 4.
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