Final answer:
The magnetic field direction in a wire coil is determined by the right-hand rule, which involves pointing your right thumb in the direction of the current; the curl of your fingers represents the magnetic field direction.
Step-by-step explanation:
The direction of the magnetic field in a current-carrying wire coil is determined by the right-hand rule. For a straight wire, if you point your right thumb in the direction of the current, your fingers curl in the direction of the concentric circular magnetic field lines surrounding the wire. When the wire is coiled, the same principle applies: your fingers point in the direction of the magnetic field while your thumb indicates the current's direction. The field is counterclockwise for the given windings, and reversing the current direction will reverse the magnetic field direction. Additionally, in a composite view, the strength of the magnetic field decreases as the distance from the wire increases, which is indicated by more widely spaced loops.
Answering another query, if a wire along the y-axis carries current in the +y-direction, the magnetic field at a point on the +x-axis near the wire will be directed out of the page towards you, represented by a dot. This is because, according to RHR-2, if your thumb points upwards in the direction of the current, your fingers will curl towards the right of the wire, indicating the field's direction at that point.