A wire carries a current of 10 A in south to north direction. The magnetic field due to 1 cm piece of wire at a point 200 cm northeast from the piece :

1.8 × 10^-9 T downwards

Maxwell's Right-Hand Thumb Rule can be used to determine the direction of magnetic field lines around a current-carrying conductor. According to this rule direction of magnetic field here is in downward direction.

Using Biot savart law magnitude of magnetic field is

$ B = \frac{\mu_0}{4\pi} \frac{I dl sin\theta}{r^2} = 10^{-7} \times \frac{ 10\times 0.01\times sin45^o}{2^2} = 1.8\times  10^{-9} T , Downward$