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(B) The maximum magnetic field $B_{\max}$ for a long straight wire occurs at its surface $(r = a)$: $B_{\max} = \frac{\mu_0 I}{2 \pi a}$. We are looki

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$[a/2, 2a]$

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(B) The maximum magnetic field $B_{\max}$ for a long straight wire occurs at its surface $(r = a)$: $B_{\max} = \frac{\mu_0 I}{2 \pi a}$. We are looking for the distances where the magnetic field is half of this value,i.e.,$B = \frac{B_{\max}}{2} = \frac{\mu_0 I}{4 \pi a}$. Inside the wire $(r Setting $B_{	ext{in}} = \frac{\mu_0 I}{4 \pi a}$,we get $\frac{\mu_0 I r}{2 \pi a^2} = \frac{\mu_0 I}{4 \pi a}$,which simplifies to $r = \frac{a}{2}$. Outside the wire $(r > a)$,the magnetic field is given by $B_{	ext{out}} = \frac{\mu_0 I}{2 \pi r}$. Setting $B_{	ext{out}} = \frac{\mu_0 I}{4 \pi a}$,we get $\frac{\mu_0 I}{2 \pi r} = \frac{\mu_0 I}{4 \pi a}$,which simplifies to $r = 2a$. Thus,the distances are $r = \frac{a}{2}$ (inside) and $r = 2a$ (outside).

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