Answer
(a) same
(b) III
Work Step by Step
(a) We know that $B=\mu_{\circ}(\frac{N}{L})I$
Now applying the given conditions, we have
$B^{\prime}=\mu_{\circ}(\frac{2N}{2L})I$
$B^{\prime}=\mu_{\circ}(\frac{N}{L})I$
$\implies B^{\prime}=B $
Thus, the magnetic field remains the same.
(b) We know that the best explanation is option (III) -- that is, the magnetic field remains the same because the number of turns per length is unchanged.
