Final answer:
The magnetic field around a current-carrying wire is circular and determined by the right-hand rule. For a wire carrying current in the +y-direction, the field at a point on the +x-axis is into the page or screen.
Step-by-step explanation:
The direction of the magnetic field surrounding a current-carrying wire is determined using the right-hand rule. Specifically, if the wire is along the y-axis and the current is moving in the +y-direction, the magnetic field at a point on the +x-axis will circle the wire in a direction defined by the right-hand rule. This method involves pointing your right thumb in the direction of the current (+y-direction in this case) and noting that your curled fingers will point in the direction of the magnetic field. Thus, for a point on the +x-axis, the magnetic field will be directed into the page or screen.
The magnetic field lines around a straight, current-carrying wire are concentric circles centered on the wire. If we use the second right-hand rule (RHR-2), with the thumb pointing in the direction of the current, the fingers wrap around the wire pointing in the direction of the magnetic field, which is tangent to the circles and has no component toward the wire. This means the field is purely circular around the wire and diminishes in strength as the distance from the wire increases, indicated by loops that are farther apart.