For points inside the wire i.e., (r $\le$ R)

Magnetic field $B = {{{\mu _0}Ir} \over {2\pi {R^2}}}$

For points outside the wire (r $\ge$ R)

Magnetic field, $B' = {{{\mu _0}I} \over {2\pi R}}$

$\therefore {B \over {B'}} = {{{{{\mu _0}I\left( {a/2} \right)} \over {2\pi {a^2}}}} \over {{{{\mu _0}I} \over {2\pi \left( {2a} \right)}}}} = 1:1$