Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be

Maximum magnetic field occurs at the surface ($$r = a$$): $$B_{\text{max}} = \frac{\mu_0 I}{2\pi a}$$

Condition given: $$B = \frac{1}{2}B_{\text{max}} = \frac{\mu_0 I}{4\pi a}$$

Inside the wire ($$r_1 < a$$):

$$B_{\text{in}} = \frac{\mu_0 I r_1}{2\pi a^2}$$

$$\frac{\mu_0 I r_1}{2\pi a^2} = \frac{\mu_0 I}{4\pi a} \implies \frac{r_1}{a} = \frac{1}{2} \implies r_1 = \frac{a}{2}$$

Outside the wire ($$r_2 > a$$):

$$B_{\text{out}} = \frac{\mu_0 I}{2\pi r_2}$$

$$\frac{\mu_0 I}{2\pi r_2} = \frac{\mu_0 I}{4\pi a} \implies r_2 = 2a$$