Answer
${\bf 750}\;\rm A$
Work Step by Step
We know that the magnetic field of a long straight current wire is given by
$$B=\dfrac{\mu_0I}{2\pi d}$$
Hence, the maximum current needed is given by
$$I_{\rm max}=\dfrac{2\pi d B_{\rm max}}{\mu_0}$$
We need to find the magnetic field at the surface of the wire which is at a distance of $d=r=1.5\;\rm mm$ where the maximum field allowed is $B_{\rm max}=0.1\;\rm T$.
$$I_{\rm max}=\dfrac{2\pi d (0.1)}{4\pi \times 10^{-7}}$$
$$I_{\rm max}=\dfrac{ (1.5\times 10^{-3}) (0.1)}{2 \times 10^{-7}}$$
$$I_{\rm max}=\color{red}{\bf 750}\;\rm A$$