Answer
$4\times 10^{-3}\ m$
Work Step by Step
We know that:
Current in the long wire $i=100\ A$
Magnitude of the magnetic field $B =5\ mT =5\times 10^{-3}\ T$
We also know that:
Magnetic field of a long straight wire $B=\frac{\mu_oi}{2\pi R}$
This can be rearranged as:
$R =\frac{\mu_oi}{2\pi B}$
Substituting and solving:
$R =\frac{(4\pi \times 10^{-7})(100\ A)}{2\pi (5\times 10^{-3}\ T)}=4\times 10^{-3}\ m$
