A long straight wire of radius '$a$' carries a steady current i.  The current is uniformly distributed across its cross section.  The ratio of the magnetic field at $a/2$  and 2$a$ is

Radius of wire $\left(R\right)=a$  
Radius of wire inside point $r=\frac{a}{2}$ 
Radius of wire out side point $r^1=2a$ 
(1) For inside point $B_i=\frac{{\mu }_{0}ir}{2\pi R^2}=\frac{{\mu }_{0}i}{4\pi a}$ 
(2)  For out side point, $B_0=\frac{{\mu }_{0}i}{2\pi r^1}=\frac{{\mu }_{0}i}{4\pi a}$  
So, $\frac{B_i}{B_0}=1$