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A long, straight conductor of radius a carries a constant current i that is spread uniformly over its cross-sectional area. What is the ratio of the magnetic field magnitude at a distance a/2 from the axis to that at a distance 2a from the axis?

1. 1/2
2. 1/4
3. 4
4. 1

Correct answer: 1

Solution

At a/2 (inside): B = mu0*i*(a/2)/(2*pi*a^2) = mu0*i/(4*pi*a). At 2a (outside): B = mu0*i/(2*pi*2a) = mu0*i/(4*pi*a). The two are equal, so the ratio is 1.

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