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Q.

A current i is uniformly distributed over the cross section of a long hollow cylindrical wire of inner radius R₁, and outer radius R₂. Magnetic field B varies with distance r from the axis of the cylinder as

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a

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b

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c

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d

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answer is B.

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Detailed Solution

Using Ampere's circuital law, B - 0 for $r \leq R_{1}$

$B = \frac{μ_{0} i}{2 π (R_{2}^{2} - R_{1}^{2})} (\frac{r^{2} - R_{1}^{2}}{r}) for R_{1} \leq r \leq R_{2} a n d B = \frac{μ_{0}}{2 π} \frac{i}{r} for r \geq R_{2} The corresponding B - r graph will be as shown in option (2).$

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