The law that gives the direction of the magnetic field due to a current-carrying conductor is Ampère's right-hand rule.

Here's how it works:

1. Point your right thumb in the direction of the current flow.

2. Curl your fingers around the conductor.

3. The direction your fingers curl represents the direction of the magnetic field lines.

This rule is a useful way to visualize and predict the direction of the magnetic field around a current-carrying wire.