Final answer:
The direction of the magnetic field at point Z, which is above a wire carrying a current from left to right, would be into the screen as determined by the right-hand rule.
Step-by-step explanation:
To determine the direction of the magnetic field at point Z due to a wire that carries a current, we can use the right-hand rule. If the wire runs left to right and carries a current in the same direction, then pointing the thumb of your right hand in the direction of the current would mean that your fingers curl in the direction of the magnetic field lines.
Therefore, for a point above the wire (point Z), your fingers would be pointing into the screen. Hence, the direction of the magnetic field at point Z would be into the screen.
The strength B of the magnetic field decreases with distance from the wire, following an inverse relationship with the radial distance r. This is mathematically represented by the Biot-Savart Law or Ampere's Law in the case of ideal long straight conductors. The direction of the magnetic field at point Z can be determined using the right-hand rule. According to the right-hand rule, if you point your right thumb in the direction of the current, the magnetic field will be in the direction in which your right fingers curl. In this case, since the wire carries a current in the direction shown, the magnetic field at point Z would be into the screen.