The force between two current-carrying conductors can be given by 

$\frac{F}{L}=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}$

where,

$F$ = force on each conductor

$L$ = Length of the conductor

$I_1, I_2$= current in the conductors

$d$ = distance between the conductors

Hence, we can say the force between two parallel current-carrying wires is independent of the radii of the wires.