According to the sources, the magnetic field produced by a long straight wire depends on whether the observation point is inside or outside the wire.

1. Inside the wire ($r < a$): The magnetic field $B$ at a distance $r$ from the axis is given by $B = \frac{\mu_0 I r}{2\pi a^2}$ . For $r = a/2$, the field is $B = \frac{\mu_0 I (a/2)}{2\pi a^2} = \frac{\mu_0 I}{4\pi a}$ .

2. Outside the wire ($r > a$): The magnetic field $B'$ at a distance $r$ from the axis is given by $B' = \frac{\mu_0 I}{2\pi r}$ . For $r = 2a$, the field is $B' = \frac{\mu_0 I}{2\pi (2a)} = \frac{\mu_0 I}{4\pi a}$ .

3. Ratio: The ratio of the magnetic fields is $B/B' = \frac{\mu_0 I / 4\pi a}{\mu_0 I / 4\pi a} = 1$.