A long straight wire of radius 'a' carries a steady current 'I'. The current is uniformly distributed across its area of cross-section. The ratio of the magnitude of magnetic field vecB_1 at a/2 and vecB_2 at distance 2a is ______.

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A long straight wire of radius 'a' carries a steady current 'I'. The current is uniformly distributed across its area of cross-section. The ratio of the magnitude of magnetic field vecB_1 at a/2 and vecB_2 at distance 2a is 1. Explanation: Consider two amperian loops of radius a/2 and 2a. Applying Ampere's circuital law for these loops. We get ointB.dL = μ_0I_{"enclosed"} For the smaller loop, `B_1 xx 2pi a/2 = mu_0 xx pia^2 1 xx (a/2)^2 mu_0I xx $\frac{1}{4}$ = (mu_0I)/4 B_1 = (mu_0I)/(4pia) B_2 xx 2pi(2a) = mu_0I B_2 = (mu_0I)/(4pia) $\therefore$ B1/B2 = (mu_0I)/(4pia) xx (4pia)/(mu_0I) = 1`

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